No, because the back-end wallet, whether it’s CoinPayments or a full node wallet, does not know about users and balances. If you were to do that, the two sites would simply share a hot wallet, but the users, deposit addresses, transactions and balances on each site would be different. The coin adapter is an abstraction for the wallet back-end, and therefore does not have any effect on how balances are stored on your MySQL DB.
It is possible to use the same CoinPayments account as a back-end for two sites but this introduces a single point of failure for both sites and is thus not recommended. You would also need to keep track of the hot balance so that it’s always enough for people to be able to perform withdrawals on both sites.
The only situation where users can share balances across sites is if you have a multisite installation and you have network-activated the wallets plugin (and all of its extensions).
Have a great year too!