score:21
Wilson's election was about a generation before scientific polling, so we don't and probably can't ever really know that.
However, it was a fact that he ran hard on that issue. Its also a fact that, knowing that he was running on that platform, the electorate voted for Wilson in 30 of 48 states. So it seems reasonable under the circumstances to consider that position the mandate of the American people at the time.
Where it gets a bit iffy is that if this were indeed a mandate, it wasn't much of one. In fact, Wilson did not receive a majority of the popular vote, and only won that by about 3%. 46.1% of the voters actually, knowing that was his main platform, voted against Wilson. So it would also be fair to consider that a very weak mandate.
The other thing that makes for a strong mandate is an unusually large electorate. The theory there is that if more voters care about the issues under contention, the winning issues have that many more voters behind them. Here, the data is a bit mixed. There were about 3 million more voters in 1916 than in 1912, but there were about 8 million more voters in 1920 than in 1916. The population of the country was of course growing at the time, so 3 million increase in voters looks more like treading water. So it doesn't appear to have been an unusually high-interest election.
So it would probably be fair to say that Wilson was elected with a weak mandate on his "America First/Kept us out of the War" platform for 1916. But it was a bare mandate, without even a majority, so it seems reasonable for him to change that position later as new events occurred.