I suppose what effect it has would depend on your relationship/understanding with the person whose money you're playing with.

If it is someone who doesn't really understand poker and the nature of short-term swings, you might feel under a lot of pressure to produce results quickly and it may have a negative effect on your game. I get fed up of trying to explain to beginners / non-players about short-term luck and long-term skill, and it seems that many simply can't understand.

If, on the other hand, the person is a friend from poker who knows your game well and justifiably has faith in you, I think it may help your game. You would not be so concerned with losing a single session and you will be able to relax a lot more.