At worst, your transaction won't be broadcasted, because it's corrupted. But rebroadcast / recreate a transaction is trivial task, so you don't need to worry about it.
OP is worried about not receiving his coins when someone else sends a transaction to his address.
@OP
As pointed out already, that is not an issue.
Your wallet does not store any coins. It only stores the private keys which are necessary to send the BTC associated to your public keys.
Whenever someone sends you some BTC, he is 'transfering ownership' of them to your public key. This is being recorded in the blockchain.
And once you want to access/send them, you need to sign a new transaction using the corresponding private key.
Your wallet does not have to be online at all when receiving coins.