Let's say your home is currently worth $200k and its payed off. Let's say you take that $100k mortgage and invest it. In the future there is a recession (or a a foreign war) and the market tanks - you're investment loses 50%. Then the bottom falls out of the housing market to the tune of 50%. Now your home is fully mortgaged (no more equity) AND you only have $50k in assets. You're so screwed it ain't funny.
I think the wise thing to do if you decided to do this would be to take a few bucks and invest in a tent - so you don't have to scramble for one when you become homeless.
Unless he's planning on living off his investments (he can't) he's not going to lose the the house. As long as he can afford to make the payments without the investment income he's ok and no one is going to loan him on his equity if he can't afford to make the payments. Pretty sure no one is going to count potential investment returns as income to pay a loan.
The markets will, eventually, recover, stock and housing. I think there are some chicken littles running around.
Now to answer the question the OP is asking I think), will he make money on it? Eventually, you might make more in interest than you are paying out in interest, but you still have to pay the principal too. So odds are you will not net anything back to you till the loan is finally paid off. As a long term investment into a safe vessel it might be ok, but I don't know that it's the best way to go. Might just be smarter to put that prospective loan payment into the market instead and eliminate the wait period of paying back the loan.
