Not if the way that I think this feature works is correct & all it does is compare your phone’s location with the location of your transaction.
In that case, if Monzo can’t pick up your phone’s location (because your phone’s switched off) it would be illogical to block the transaction, just because Monzo don’t know where you are. Instead, I assume that Monzo’s other fraud detection rules (which are active regardless of whether location sharing is switched on) will kick in.
I explained my theory (I could be wrong about this) in more detail here -
If I was wrong though, I expect we’d have seen posts / tweets about transactions randomly being declined by now, from users already who’ve been caught out by this issue, as obviously people’s phone’s run out of battery quite a lot…