In most cases, it doesn't seem right to continue. I just resign. An early blunder could warrant some excessive play for the sake of actually playing the game.
However, if the pieces are exceptionally weird, yes, it can justify playing on in a technically lost position.
I am happy to oblige an opponent who wishes to play on if they've lost, except if the skill difference is too great.
If a position is hopelessly lost, then I resign. If I'm checkmated soon I might play out the mate.
However, if there is some hope left I play on. Variants tend to add some dynamics and that makes turning the tables more likely.
I think it is important to not prematurely resign. If you "think" you are lost, but ultimately you are not familiar with the game enough to tell, then play on. For beginner chess players I think never resigning is a good tip and that applies to beginners to chess variants too. Don't resign for losing a lot of material, resign when your position is hopeless.
I think in general the more different a variant is from standard chess, the more likely I am to play on in a lost position, with part of the reasoning being that I'm more likely to learn something new from playing on in a lost position, if I'm playing a variant, than if I'm playing standard chess. Would you say that you are also more likely to play on until mate if you are playing a chess variant than if you are playing standard chess?