I fear there is a confusion with the tenses. I don’t know if he will is all right but I don’t know if he would is backwards and forwards at the same time. What you need is: I didn’t know if he would.
Stretches the mind a bit too much for me and I can’t really accept the notion of ‘when asked to’ I’d have to embroider it a bit and say: I really don’t know if he would be likely to buy coffee . but no doubt someone will shoot me down in flames!
I don’t think we can rule out a possible use of ‘would’ in combination with “I really don’t know if…”, but your sentence probably isn’t the best example for doing it, Tom (especially without any context). If you added the word ‘that’, for example, it might be more palatable as a “stand-alone” combination:
I simply think the combination is possible. Is it the combination that you consider to be far-fetched or is it only Tom’s particular sentence? I’ve already agreed that Tom’s example isn’t particularly good with the combination (without additional context or words).
Let’s add another word to Tom’s sentence: I really don’t know if he would ever buy that coffee.
Or, let’s look at a different sentence: I really don’t know if he would lie.