If you use Wasabi Wallet version 2, take note CoinJoin now happen automatically. If you didn't disable it manually before the wallet receive coin, it's possible your coin already went through CoinJoin probably without you knowing.
Yes, but with a caveat.
Coinbase has always been known to intentionally mark and restrict transactions associated with gambling sites, illicit marketplace and anything in that category. They also openly deduce and blacklist CoinJoin transactions which Wasabi is able to do. If you use CoinJoin, you can potentially run the risk of that happening. You can have plausible deniability if you use another wallet before that and argue that the CoinJoin isn't related to you.
And while other exchange usually isn't as strict as CoinBase, deposit mixed/coinjoined still lead to trouble (e.g. account frozen, asking privacy invasive question). OP should using P2P or decentralized exchange instead if he don't mind lower volume and sometimes less favorable exchange rate.