If the MVP system is going to be similar in actual use by players to the one used in SWTOR PvP, as I'm fairly certain it will be, I don't think anyone is going to care after the first week or so. Most of us would only occasionally pick someone with the intent of giving them a MVP medal. The rest of the time, people would either just leave without voting (thus meaning they couldn't be voted for as well) or randomly choose someone to throw a medal at. Every medal you got added a bonus to your reward, so even if just 1 person chose you for MVP, you'd walk out with a small extra something. It was harmless and just gave people an opportunity to be charitable without spending more than a couple seconds.

In other words, the MVP system will do nothing but potentially give you a bonus. It will not hurt you in any way.