Assuming you are talking about an SHA256 miner, yes it can be profitable if you have the patience and don't mind entering the morally grey territory of mining ninja launched SHA256 altcoins. One out of 100 of those may end up being legit, most are just short lived shitcoins. Unless you have very cheap electricity it is doubtful that mining BTC with it will gain you your ROI.
Good point you've raised. Almost any "home miner" I have come across are ninja mining any number of sudden-rise alts. If you even take the time to look back old threads, you might see that some of today's crazy pump alts were mined months or over a year ago. I'm beginning to think even the lousy prices most will only ever get for a few days seems worth it for those miners.
