david:
I'm wearing an M&P40C right now.... But in a DeSantis OWB....
No reason why you couldn't put yours in a pocket, but by itself, or in a pocket holster of some kind. Safe enough, IMHO, if there's nothing else in your pocket, but otherwise you need the holster to keep "stuff" out of the trigger guard.
It is kinda big, but probably not a lot worse than a J-frame.
I'm big enough (and old enough) that a square bottom shirt worn outside of my belt (Wilderness Trainer in "dress" clothes) lets me get away with about anything:
....
(OK, it's not an M&P40C, but I use an essentially identical holster for that. This one's a 5" Para PX745EM. It really is blue, btw....)
(Lest we start the "CCW Badge" wars, I'm a semi-retired rent-a-cop, and helped found the agency back in the late 60's. The badge is legitimate, although it doesn't convey a lot of authority anymore. After more than 40 years of carrying it, I just keep on doing so. I figure I'd lose it if I took it off

.)
If, btw, you can stand and IWB, a good leather one with a protective top (you don't necessarily need a top strap, but you do need something between your gun and your skin on the inside) should work well if you can wear some sort of cover garment. "Tuckables", "SmartCarry", or the pocket gear will handle the rest, and the compact M&P's are close enough....
Regards,