Is it useful (and polite) to ask a potential meditation teacher about their attainments?

The Buddha while he was a Bodhisattva did directly ask his teachers "So I went to him and said, 'To what extent do you declare that you have entered & dwell in this Dhamma?' When this was said, he declared the dimension of..." (Ariyapariyesana Sutta MN 26)

It is important to understand what is it that the teacher is proficient in teaching, his/her personal experience and experience as a teacher, method(s) of practice etc. Meditation teachers also have to be honest and open with their experience (attainments are mere labels) do they teach with direct experience or mere faith in a certain teaching, or because they like to teach, or because its a tradition of his Bhikkhu lineage, etc. Somewhat similar to how you would go about selecting a teacher for another subject.

The Canki Sutta MN 95 gives a method of discovering via observation the worthiness of a potential teacher. However it will take time.

"There is the case, Bharadvaja, where a monk lives in dependence on a certain village or town. Then a householder or householder's son goes to him and observes him with regard to three mental qualities — qualities based on greed, qualities based on aversion, qualities based on delusion: 'Are there in this venerable one any such qualities based on greed that, with his mind overcome by these qualities, he might say, "I know," while not knowing, or say, "I see," while not seeing; or that he might urge another to act in a way that was for his/her long-term harm & pain?' As he observes him, he comes to know, 'There are in this venerable one no such qualities based on greed... His bodily behavior & verbal behavior are those of one not greedy. And the Dhamma he teaches is deep, hard to see, hard to realize, tranquil, refined, beyond the scope of conjecture, subtle, to-be-experienced by the wise. This Dhamma can't easily be taught by a person who's greedy..."

Here's very neat zen answer by Venerable Chong An Sunim to question about attainment. It might give you some new perspective. https://youtu.be/hOZKvRMBdAM?t=23m45s

If it's a monk they are forbidden from discussing attainments with lay persons due to some monks at the time of the Buddha using their attainments and powers unskillfully with lay persons.

Otherwise it's still not something you ask the person directly, although it appears to happen quite often as I've seen it on many Dhamma talk videos and in person at retreats. Usually the person says flat out no or redirects the question in some way or another.

It may also be useful to observe your desire to have a teacher that matches your criteria and the judgments, expectations, and issues that arise from that.

It's like asking what's your ATM security key. You might share it with a family member because they are your family and you trust them. Just like that, an Ariya Puggala might discuss his attainment with the Buddha or with Arya Sangha. But they wouldn't discuss it with ordinary lay people. You could observe the teacher's behavior for a while and see if he becomes angry or afraid. If he does, then at most he could be a Sakadagami. But even if he doesn't show his anger, he could still be getting irritated inside. So it's difficult to tell if one has attained a certain stage of enlightenment. But it's easier to tell whether one is not an Arahath. One of the methods I use is to see if my level of understanding, appreciation and confidence of the Triple Gem improves after listening to a sermon from a teacher. Sometimes you might listen to a teacher who might have memorised a lot from Tipitaka and the Commentaries, but when interpreting the meanings, he might make you doubtful of the Triple Gem. Sometimes you see certain teachers even going to the extent of insulting the authors of commentaries and questioning the authenticity of Abhidhamma to prove their point. That's a clear indication that you should look for a new teacher.

With meditation, you can practice it and observe your mind to see if your defilements are subsiding and being eliminated. If they do, the technique works and the teacher is good.

Yes, an unenlightened teacher with a sharp knowledge can still make someone else enlightened by giving a good sermon. But it's still won't be as good as having instructions from an enlightened person. Even with an enlightened teacher, you may not be able to be successful. Even the chief disciple most venerable Sariputta thera couldn't help a certain meditation student. Only after taking him to the Buddha, was he able to attain enlightenment. Only the Buddha can give you the instructions that will suit your personality 100%.

So I'd stop focusing too much on finding the teacher's attainment and observe myself to see if the practice works.

Worrying about whether something is polite or not is a hindrance. I am sure some practitioners would find it offensive but if they are offended that probably tells you all you need to know.

If you have yet to obtain the Jhanas then there are probably others who are still more advanced than you who have not yet obtained them either. The way I see it, anyone who is beyond you can be a good teacher and anyone who you are beyond can be a good student.

According to the Thana Sutta:

It's through living together that a person's virtue may be known, and then only after a long period...

It's through dealing with a person that his purity may be known, and then only after a long period...

It's through adversity that a person's endurance may be known, and then only after a long period...

It's through discussion that a person's discernment may be known, and then only after a long period...

You can't really know simply by asking.