You'd have to give it a try to make sure. I would believe that it will only inject the routes from protocol A that are installed in the RIB because the other one may not be OK to redistribute. Taking EIGRP as an example, if there are 3 different paths for a given route and all have different metrics, the redistribution router (autonomous system border router - ASBR) will himself be the next best hop for that route distributed in protocol B. So even if it has 3 entries to a route (default route for example), it will be the best hop out of protocol B's domain on its way to the final destination.
HTH
Olivier Martin