Yes, short term scheduler can put up processes from Ready Q to CPU, provided that there are processes waiting in Ready Q. In fact, that is what happens in most of the cases.
For example, if we have got 64 processes (in total including ready Q and the one in already using CPU), and if somehow 3 processes go into deadlock(while waiting outside after acquiring a part of their resources), it will be they who will be waiting outside and not getting the CPU. Why should rest 60 be devoid of opportunity to use CPU. So, CPU won't just sit around. It will actually execute other guys in Ready Q, while there is deadlock already happening simultaneously.
It's just those 3 processes going into deadlock, not the whole system. The whole system in deadlock means either a very crucial process(say kernel) is stuck in deadlock or all (literally all) processes are in a deadlock.
In theory, we just study just take 2 or 3 processes and the CPU is rendered unusable as supposedly there are no other processes we have considered, but the reality is quite different. There are surely many other processes which will be scheduled while these 2 or 3 guys are still in a deadlock. Let them be and give the CPU to others. Simple!