I have an account on Coinbase and have an ETH Wallet with them. If someone sends their ERC20 token, will there be any issues receiving it?
There's nothing technically CoinBase could do to stop someone from sending tokens to one of their addresses--that transfer takes place in the token contract and can be initiated by the sending account, and the 'record' of that transfer is stored in the token contract's balance map.
You do not want to send your tokens to Coinbase, however, for a least two reasons. First, they hold the private key of your account. If you needed to later send the tokens out of that account, the only way to do that would be to ask them kindly to do it for you. The second reason is, as far as I know, they do not provide an interface to deal with tokens. If they did, then maybe you would be able to send the tokens out, but without it, the token would be stuck in there forever.
I think I answered your question. If I misunderstood, please let me know and I will remove this answer and let someone else take a shot.