If you consider a breach of the service and passwords are properly handled on the authenticating side, the attacker who gained access to the password database is left only with the brute-force attack.
Brute-force attack means checking exhaustively all possibilities, but does not limit the method to the dumbest "from 0000 to ZZZZ" one. That said, an attacker who expects users might create multiple accounts with the same password can easily modify the algorithm to check all accounts against each discovered password.
Whether this is an issue depends on you.
If you consider an attack on the client side, an attacker needs to learn one password from among multiple account-password pairs to learn all of them.
If you login to all accounts from the same machine, the attack surface remains constant, but if you use one account on a mobile device, the other on a secure PC, then one compromised device reveals the information about all accounts.
Again, given that you expressed the idea means other people think of it or do it too, and an attacker would probably take advantage of that (the cost is nil).
Whether this is an issue depends on you.
