Will recurring contributions be recorded for memberships not hosted by CiviCRM?
Civi will not record contributions for PayPal recurring contributions that aren't set up through CiviCRM.

Broadly speaking, there are two types of payment processors when it comes to recurring contributions - those that rely on webhooks and those that rely on tokens.  Most webhook-based processors call the webhook the IPN ("Instant Payment Notification") address.

With IPN processors (like Stripe/PayPal), when you create a recurring donation, CiviCRM sends some info to the processor (amount, how often to charge, the CiviCRM contact ID, the recurring payment ID, etc.).  

When the payments are processed on PayPal's end, the processor will push some data to a URL that Civi has set up explicitly for the purpose (the "IPN URL").  So Civi won't create payments until PayPal says, "Hey, we processed this and it succeeded or failed".  PayPal relies on the info that Civi sent to PayPal when the payment was created to send data back to Civi - so non-Civi recurring donations won't work, because, e.g., PayPal doesn't know the contact ID to send in its IPN.

So one option is to record the payments manually each month.  The other is to investigate whether you can shoehorn the Offline Recurring Payment extension to fit your needs.  Note, however, that the extension isn't tested on modern versions of Civi and is for a slightly different use case - so unless you are (or have access to) a coder, this might not be a good choice.