Yeah, an example would be, your in the small blind and the big blind folds more than 50% of hands, we min raise any two cards and show a profit long term. I should have made a button example since you loose long term from the small blind... Lol... You can make a button example.
I think the answer is yes. For example, if I only raise TT+, 72o for 3 big blinds on the button, then 72o will probably be profitable even vs the best counter strategy. However, the loss of value due to all the other hands that I'm folding would be so detrimental to my winrate that the inclusion of 72o in my range is merely a novelty.
The answer is no without other stipulations. This should be completely obvious. Of course you can devise scenarios where the answer is yes, but absent other information it can only be no.
I think in many scenarios you can show a profit with really poor hands, but it's a long term game so eventually you are gonna get bit and lose more than just mucking it from the start. It's hard to make equity with good hands, so I'm pretty much done with the ones i have no chance with.