If 3 find out about it then yep, your insurance would probably be void.
I had it the other way round i needed another phone for my 3 sim card as i broke my phone, got an unlocked phone off of ebay, 3 found out somehow that i wasn't using their phone and blocked my sim card and phone....
i'd suggest that they may be able to find out that you are using their phone with an different simcard and would probably do the same thing.
P.S, coverage for three is absolutely terrible where i live, i only have to wait another two months til i'm out of the contract, yippee!!