Is a moral society more open to the gospel than an immoral one?

The simple answer is, it could go either way. A moral society could relate more easily to the message of the gospel, understand it better than an immoral one, and therefore be more open to it. Or a moral society could believe itself to be self sufficient and adopt the "we have our morals, we don't need God" attitude.

Ultimately though you do have to question, as Richard does, where the morals in this hypothetical moral society originate from, and what you mean by moral. There are some societies in which it is seen as immoral to eat the meat from certain animals, but other societies that self-identify as moral would have no issue with that. Most of us would think of cannibalism as immoral yet there are tribes which have a moral code that allows them to eat other humans. So which set of morals are we using to define what is moral and immoral?

Since this is Christianity.SE, we can take morality in this case too mean Christian morality. In which case it is moral to accept the gospel and immoral to reject God - so a moral society will have already accepted the gospel or at least be fully open to it.

My counter question: what would be the source of the morals for a "moral" society?

People don't--on their own--behave in a moral manner. I would contend that a moral society is one driven by a moral standard outlined by a specific religion.

To break this down even more clearly: a moral society is driven by a set of morals. Sets of morals are driving by a particular religion. I don't believe that you can have a good, solid set of universal morals that are commonly accepted by a wide group of people unless it has a religious backing.

Now to the heart of the matter: What religion is this theoretical, moral society driven by?

If this theoretical society is driven by Christianity, then clearly the society will be more open to the gospel. However, if this moral society is driven by, for arguments sake, Buddhism, then the society will be less open to the gospel.

However, I contend that you cannot have a moral society without having a religious society. The religion of the society will determine the openness to the gospel.

This question is particularly difficult to answer because it is not clear who should evaluate what is moral. If Biblical morality is the standard, then I strongly suspect that it would "encourage" openness to the Gospel for the trivial reason that there isn't much reason to adopt those features of Biblical morality that are not found in other moral systems unless you're already predisposed to the Gospel.

If the society gets to self-define what is moral, as long as it doesn't radically violate moral norms that are shared across most religious and ethnic groups, then we might look instead to things like crime rates, self-reported happiness, and so on. These measures do not paint a clear picture, although it is clear at least that there are non-Christian societies that have relatively low crime and reasonably high happiness (e.g. Japan) which do not seem to be massively adopting Christianity. So I think tentatively the answer might be not necessarily.

The Jews of Jesus's time were not particularly moral; they were particularly moralistic. They went to great lengths to put on outward appearances of piety, which repeatedly earned them the condemnatory epithet of "hypocrites!" from the Savior. We get a pretty good sense of what they were like from the Gospels. For example, using legalistic tricks to get out of caring for their parents by instead being able to (very visibly) donate the money to the temple, "and many such like things":

Mark 7:8-13

8 For laying aside the commandment of God, ye hold the tradition of men, as the washing of pots and cups: and many other such like things ye do.

9 And he said unto them, Full well ye reject the commandment of God, that ye may keep your own tradition.

10 For Moses said, Honour thy father and thy mother; and, Whoso curseth father or mother, let him die the death:

11 But ye say, If a man shall say to his father or mother, It is Corban, that is to say, a gift, by whatsoever thou mightest be profited by me; he shall be free.

12 And ye suffer him no more to do ought for his father or his mother;

13 Making the word of God of none effect through your tradition, which ye have delivered: and many such like things do ye.

Remember that by the end of Jesus's life, he'd become such an annoyance to the political rule of the various factions of Rabbis that they paid off a traitor to help apprehend him, explicitly sought for false witnesses to find a way to charge him, convicted him of blasphemy in a trial in which practically every point of procedure was illegal under Jewish law. Once he had been convicted of blasphemy, they wanted to put him to death, but only the Romans could enforce capital punishment, and as polytheists they didn't really have much of a concept of "blasphemy," so they had no compunction against hauling him before Roman authorities and changing his charge to the highest crime that Rome accepted: treason. When he was interviewed by the Roman authority (Pilate) and found not guilty, they pressured him and even threatened to have him charged with treason by higher Roman authorities if he wouldn't play along. (And historians suggest they'd have had a good chance of making the charges stick, so he had to give in to save his own hide.)

These were the people in charge of the "moral society" of Jews ~30 AD, making the rules and setting the example for the common people to follow. Not a particularly good example of moral people, in my opinion.

As for standing out as an alternative to the status quo, yes, that's true, but the other side of that is that Christianity requires repentance, which involves changing one's ways. It's one thing to say "wow, those Christians are really cool, I wish I could be like them," and another to actually sincerely try to give up all your sins, especially when it impacts your relationship with your friends and family.

Matthew 19:29

29 And every one that hath forsaken houses, or brethren, or sisters, or father, or mother, or wife, or children, or lands, for my name’s sake, shall receive an hundredfold, and shall inherit everlasting life.

Jesus didn't say this just to sound cool; he said it because it was a very real possibility of what might be required in order to truly live the Gospel.

In Romans, Paul mentions that the Gentiles can do good, because the morals are written on their heart.

Romans 2:14-15 NIV
14 (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. 15 They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.)

I believe that a society which follows these morals written by God on their hearts are more likely to accept the Gospel. When introduced to the Gospel, they are likely to see it as the truth since they have already accepted the morals it teaches.

Before they accept the Gospel, though, they are not judged by these laws, but will perish as all others who do not follow God's law. (Romans 2:12)