Yes. If you are using another membership plugin and you have existing accounts with payment vendors, you can use those same accounts with MemberMouse. However... you will need to be aware of the way that an integration with a payment vendor works, because while you can use the same account, your members' billing information cannot be transferred.
When you configure your MemberMouse site to work with a payment vendor, you are establishing a two way connection between your site and that vendor. The key to that connection is a transaction ID that is created by MemberMouse for every transaction. It is this unique transaction ID that MemberMouse transmits to your payment vendor along with the member's payment details and billing instructions. Inversely, when a successful payment is received to the vendor, it transmits back to MM that confirmation, using the transaction ID to specific what the payment was for.
When you migrate your users over from another membership plugin, the one thing that MemberMouse cannot do is capture the transaction IDs used by your previous plugin. In the import wizard template, you are setting each member up with specific settings; what products they have, what membership level they have, etc. But because those purchased did not originate within MemberMouse, there is no transaction ID associated with them.
The only time this is relevant is when a member, who has a recurring billing product, attempts to cancel their account or subscription, or if a payment is missed. If a customer cancels their account in MemberMouse on a product that was purchased initially via MemberMouse, MM will transmit to your payment vendor a request to cancel any recurring billing for that member associated with that specific transaction ID. Because that ID exists within the payment vendor, then the billing is cancelled. But for imported members, there is no transaction ID, and thus no way for MM to tell your vendor to cancel. The same is true in reverse order, if a member cancels any billing via their payment account (usually this happens only in PayPal), then the payment vendor will transmit back to MM a request to cancel and a transaction ID, which does not exist in MM, and thus no action is taken. The same action takes place on missed payment (say if a member cancels their PayPal account, or there are insufficient funds)
There are several ways clients have addressed this situations. Depending on the size of your membership list, some members have requested imported members to re-sign up via MemberMouse, so that the direct connection between can again be established. Other customers have created a specific membership level for these members. Then, via a Push Notification when a membership or bundle is cancelled, the admin will know to go into their payment vendor and manually cancel any recurring billing. One recommended method of handling billing when migrating is addressed in this article: Migrate Members from an Existing Membership Site