Can one still apply for recruiter while under suspension of favorable actions?

SGT (Join to see) if one is under investigation, then they should be flagged. There is a flag code for it. Para 2-2 AR 600-8-2 Codes L, M, A, U or V MAY apply (I say again MAY). Depends on the particulars which I DO NOT WANT TO KNOW.

If you are flagged, attending an Army School is favorable action. I can't see that application going further than the round file. They really go through the person's file. I know from experience of a soldier in my command that was under investigation and deemed clear by me, IG and EO, the mere appearance of a violation deadlined his application. See Unfavorable Status definition on page 31 of the regulation in Glossary Section II.

Any flag for investigation is a non-transferable flag: you cannot transfer until the flag is lifted. You cannot attend a school under any kind of flag.
Another factor to consider:
Position of Significant Trust and Authority (POSTA) is a suitability screening mandated by the Secretary of the Army for Recruiters, and several other positions.
It's likely that the subject matter of an investigation would preclude a Soldier from passing a POSTA screening unless they were exonerated in that investigation.