I don't think that will be a problem. I understand we've got some fans of the same team, but this is really just for fun.
If you are assigned one team, you will give a better look at their needs and their likely pick. This, I think, will create a very accurate mock draft.
Plus, you get to say I told you so when your pick is right. I think last year I got Carr, Peppers, Henderson, and Will Green right.