Would branch release me if I volunteer to be a recruiter?

You will not be released prior to serving you assignment, generally 2/3’s. You can submit to be accepted in recruiting, howeverbyhe assignments are based on open positions, you may not get any closer to your hometown. It is a process. Thank you for your service.

Your branch absolutely cannot release you with less than one year on station. That waiver requires approval from the Commanding General of HRC. Even when the Army was struggling to fill all the recruiters spots by the middle of January, they could only wave time on station down to one year.
As a Sergeant First Class you are going to be much less likely to be approved for recruiting. Especially, in your MOS. With as low density as your MOS is, it creates a significant impact to lose a Sergeant First Class from your career field for three years.
Recruiting could put you post your hometown, but it could also put you much farther away. There is no guarantee where you will go as a recruiter, and your desires have no bearing against the needs Recruiting Command

So there are really two major things that hurt you. The first already mentioned is the fact that you have not been on station long enough. The second and perhaps the most important is the fact that you are a SFC. Now that doesn't mean you cannot do it, but depending on when you may get looked at for MSG, odds are you would not be selected. They want SGT-SSG(non-promotable) to fill a majority of the ranks in what we call Non-Prior Service recruiting....or enlisted. The reason why is SFCs are Center Leaders and run the recruiting centers. There are never a majority of SFC in centers and with you potentially going to the board for MSG, you would be considered too far along in your career. Keep in mind, recruiting is a broadening assignment and meant to develop younger NCOs for promotion to senior Enlisted Soldiers. I should also mention like what was said before, the odds of you being anywhere close to your hometown are slim to none. You might get the same state, but again odds are not in your favor for that. Also you would have to go to the ARC(Army Recruiting Course) which was 7 weeks at Ft. Knox, may be longer now....