The short answer is yes! Grandfather, grandmother, brother, whomever! In fact anyone can get your relative's FBI personnel file as long as they are either deceased or sign a waiver if living. The long answer is it may take quite a few months to process. But I strongly suggest you do it, especially if you're seeking records going back to the 1920s, 30s, etc. We don't know how long these records are going to be around and you don't want to miss out on some true documented history!
The personnel files of these men are rich in family history in addition to the agent's career. The application alone filed for employment with the FBI will provide a much needed background for many who are seeking detailed facts about the agent's early family life, immediate members, relatives, education and much more. The background investigation done will reveal friends, associates and even high ranking members of the government who may have known the applicant.
For those of you interested, I've prepared a short "how to" document giving you the necessary info to make application for the information with the FBI and what to expect. Want a copy? All you have to do is ask. Just send me an email via this site and I'll forward you the document.