So before you get this set up, you might end up buying a third scavenger or a 4th stash anyway. In which case the following is moot. However, it's probability time.

The chances of colliding scavengers once this is set up is 1 in deck size - 4. Or for our purposes, P(No Collision) = (d-5)/(d-4), where d is total deck size. So let's say we have a kingdom where there are no extra buys and we set up by turn 10 so we have a 19 card deck. Then P(NC)=.933 for that turn. If we assume the deck grows by 1 each turn, then the cumulative probability of no collision is P_{cum,n}=P_{cum,n-1}*(d_{n}-5)/(d_{n}-4), where d_{n} is the deck size on turn n. So you get 4 provinces before a problem 77.8% of the time, 5 provinces 73.7% of the time and all 8 provinces 63.6% of the time.

So odds are good that you won't have any issues once you get set up. But it's really bad to miss early here, because you need to go through your whole deck before you can hit province (most likely) again. So I would say, try to foolproof this strategy early with an extra scavenger or stash, but once you start buying provinces, just start greening and hope for no bad luck.

/math