It depends on a lot of factors:
Your hearing, your training/experience relative to compression artifacts, program material, equipment, ambient noise, blood alcohol level

....
In theory, there should not be any perceptible difference on 99+% of material to most people, somewhat lower for perceptive people.
Since APE is identical to the original wave, this question is really: can you hear the difference between LAME --alt-preset insane and the original WAV file.
Suggestion: try it for yourself, but be sure to use ABX methodology so the placebo effect doesn't bias you.