Based on my experience they won't cover check rides. Unless you have different info than I do, or personally spoke with someone at the VA (after holding for over an hour I would guess).
I completed my Instrument, Commercial Single/Multiengine, CFI/CFII/MEI using Chapter 30 benefits (Montgomery GI Bill) through part 141, and they wouldn't reimburse ANY of my written tests or check rides... Would love to know if ATP is different, because I still have some benefit remaining and I am getting close to that point. Anyone else have any real experience with this specific situation.
I apologize this isn't a direct answer to your question... A side note... for some reason they DID reimburse for my 3 A&P writtens (but not the practical).