Forensic psychiatrist here. It probably won’t cause a problem for hiring at most places.
I would, however, strongly recommend considering just taking general boards in the beginning of your fellowship year. It is what most people do and very achievable. Beyond that, there is basically no overlap between the general and forensic psychiatry boards. There is little utility in taking them together and studying for both at the same time sounds terrible to me. Pass rates notwithstanding, most people find the forensic exam more difficult than the general exam, and it definitely requires more specifically directed study of information you did not get from residency and, depending on how/how much your fellowship drills cases, may not have gotten from fellowship either. Forensics is also only offered every two years, so if you overextend yourself and fail forensics, you have to wait a while for another opportunity.