That's what I thought. IIRC, it is a bip39 compatible HD wallet, correct?
Yes.
Don't you have to send a transaction to the Join Coordinator server, and if so and it's rejected, what happens to that transaction?
When you coinjoin, the server you use, which works as a portal for those who want to mix, requires you to send it your UTXOs, that will be used as inputs for the coinjoin transaction. So, it's down to the server. If the server doesn't agree to pass your UTXOs, you won't participate in the coinjoin.