They won't be in a landlocked lake in large numbers for very long unless stocked by the state. While true that under the best conditions they can reproduce, in a lake where they can't get to a constantly flowing tailrace (almost any lake), they won't self-sustain.
If they came over the dam, they'll probably die out. After the spawn, it's not uncommon to see larger ones floating as they attempted to fulfill their biological directive for the last time. I've caught stripers, white bass, white perch and what I would bet are hybrids all in one day. But hybrids were not stocked on that lake and white bass had long been presumed displaced by the perch. I asked an SCDNR fisheries manager about it and he told me they do go over dams in large numbers occasionally.
My guess is same as yours. People know they aren't supposed to be there and tossed them. Check with DNR and proceed. You might be able to keep them all if you catch a mess. They taste great, like an ocean fish such as grouper. If they've gotten easy to catch it's probably because they're competing with bass for limited resources. But their time is short. Try the tailrace when the water temp is creeping into the 60's and the dam is generating.