If the power is free then you are going to make money, no questions asked really.
If you consider the hardware you have to buy in order to set up the mining operation, is that even true? I have not mined any coin in my life, but I've been doing some research about it and from all that I've seen the income you get from mining solo with cards and the like is minimal. Even with free electricity, you would have to recoup the cost of the mining equipment. Is that actually possible by doing what op is proposing?
But if there is a choice to get profit in a liquid token or double profit in shitcoin I would choose liquidity.
That is actually an excellent point, but I would assume that a higher profit coin would also have enough liquidity in the market such that you could sell it easily. You certainly wouldn't want to mine a coin that isn't listed on exchanges and that no one is interested in.
Best of luck to op if he tries this.