Yes, that is worthwhile trying. Even though this isn’t directly your case, do give this bit a read. This because, in general it is the case that bias field correction and brain mask estimation (or skull stripping) are often very dependent on each other; which means that if one bit is messed up, the other might be as well. So in your case, I would certainly give it a go, and see if it improves things.
This depends on what you’re doing with those images afterwards. If your suggestion does work, you could try to do this the same for all subjects. You could also then actually provide the resulting brain mask to N4, which will then likely even perform correctly. So, potentially, you’d just be reversing the order of the skull stripping and N4 in your pipeline, for all subjects.
But it’s definitely a thing that’s up to experimentation with your data at hand. I’ve seen different performance of different kinds of data in other peoples’ cases.