Depends on the shelter....most make you pay up front for a spay/neuter when adopting. Dogs that are reclaimed are usually never s/n'd during the hold time.
But I know a few shelters that will order it if the dog is picked up more than 2x's. And the reclaim fee's are higher, or fines given. That is one reason many in my county don't reclaim, they don't want to pay for getting their dogs out of jail, so just leave them there