I think it's a big assumption, but not without some merit.
Firstly, we don't know if there are truly random events at all. To say that an event is random means that we don't have sufficient information (and method of calculation) to determine the exact outcome. But we cannot be absolutely certain that such information doesn't exist (e.g. some yet-to-be-discovered hidden variables) or may not eventually become available to us.
So, one can at least reasonably entertain the possibility that there are no truly random events at all -- and in this case, there wouldn't be any random processes in the brain (and decision-making, etc), either.
Secondly, to quote George Musser (in reference to Butterfield, Dennett and List), "human cognition involves different structures than atomic physics and is governed by different laws, so determinism at micro level need not imply determinism at the agential level." As an analogy, if you consider a process like gas expansion, the behavior of individual particles may be random, but certain "important" aspects of the "overall" behavior of the system are quite deterministic.
So, in this case as well, it may be possible to view the brain as a deterministic mechanism (perhaps to some extremely high degree of accuracy) on the level of decision-making, even if you allow random events on a small scale.
Now, as to your last question, if we were to grant that the decision-making mechanism is "truly" random, then it's very difficult to reconcile it with (at-least) a common-sense meaning of free-will. In this (common) sense, free-will implies "control" over the choice being made. However, if the decision-making mechanism is random, then to talk of "control" is (nearly) as meaningless as in the case when your decisions are determined by material/physical factors. So, at the very least you'd have to redefine the meaning/scope of "free will". Of course, people are certainly trying -- and it's worth reading about (here's one overview: https://www.scientificamerican.com/article/quantum-physics-free-will/).