I don't think that it would be that big of a deal. If anything, I think pitch selection for relievers is more forgiving (since the batter hasn't seen their stuff before, and most relievers get away with throwing a lot of fastballs) and that most starters would perform better as a long reliever. I guess there could be issues in terms of adjusting to the role - how long they can pitch, etc, but personally I don't find it to be a big deal.
Of course, this is your long reliever, so it's not exactly the most important role to fill. They'll only be pitching if your starter sucked - in which case, you'll probably be on your way to losing anyway - or if your starter blew out his arm.