Will this hold a man door from the garage to the outside?

No, this will not fix a jamb on the hinge side. This is specifically to repair or reinforce a jamb where the latch/deadbolt engages the jamb. The thickness of this product would most likely interfere with the hinge clearance.

In my opinion, yes this will make a good replacement and reinforcement for the broken door jamb. I just installed it on my front door and it is very solid.