It's not a good idea to do this with a non-deterministic wallet. Each time you send bitcoins, bitcoin-qt generates new private keys to add to the key pool. These are entirely random. Eventually the two wallet copies will diverge and you'll have different private keys in them. It'll be very confusing and you risk loosing bitcoins.
If you want to share a wallet on different computers use either a web wallet or a deterministic one like electrum.
Please listen to this very good advice.
I considered the OP's question to be hypothetical but now, reading it over again, it looks like this is something they might be thinking about actually doing.
Can I run the same wallet on multiple computer at the same time? Anyone know? thanks.
DO NOT DO THIS for the reasons stated above. It can be done but a) you really have to know what you are doing and b) it cannot be done with the bitcoin-qt wallet.