(disclaimer: I haven't tried that myself, with this post I just want to give you some help based on what I've read in the specs, given there are no other replies so far, so FWIW)
As far as I can see in the docs for these drives, they don't require any special handling or drivers in Linux, coupled with the fact that the mPCIe slot on the board is, well, just a normal mPCIe slot - I believe you should be just fine.
I would definitely recommend you to negotiate some moneyback option - just in case my theoretical speculation above is proven to be wrong by the hard reality :-) And if you go for that - please report back here the actual outcome, I believe this information would be very useful for a lot of people.
I am now looking into mPCIe SSD options for the Galileo. Did you have any success you can report on? I was thinking something cheap like below: