What advice do you have for someone who is looking to drop a recruiter packet as an E-5?

I would first ask how long you have been an E5 and have you fully qualified? If you have less than 24 months TIG now recruiting may hurt more than it helps. Specialty assignments are great for the Army, and great for the individuals who excel, other than that it is a dog eat dog world out there. Recruiters compete with corporations, schools and a multitude of other opportunities. It is not easy. Seek an office call with your CSM, glean his advice as he or she can review your background, current performance and gage your ability to excel in that environment.

As for the Battalions ability to stop a packet, there are a few ways they can do it. That is why you should ask for the office call with the CSM.

They can't stop you, but they can say no to it . It still has to go forward though.

Nobody can stop you from emailing your packet to HRC, but since you need a Commander's interview with your Battalion Commander for your packet, you probably will not get accepted. But then again, if you're a SGT in your unit and your Commanders dislike you enough to block your recruiting packet, you need to reevaluate your professional life choices. Of course, if you're not promotable it won't matter anyway, branches usually won't touch you till you're at least promotable.