Yes, they can, and do. Appropriations bills are extremely detailed. Each program has to be separately authorized. The agencies and departments have very little

Yes, they can, and do. Appropriations bills are extremely detailed. Each program has to be separately authorized. The agencies and departments have very little flexibility to move money around according to their own priorities. There's a circular dependence. Congress has to pass the authorization bills, but it starts with the President's budget request, which in turn is authored by the separate agencies. Congress routinely declares the President's budget "dead on arrival" and sets about writing its own, which usually starts from the last year's budget. In reality there's a lot of jockeying, with the individual department meeting with individual Congressmen and committees to stress their priorities. At least, they used to. I have no idea what happens now.