In summary, yes
What you have described is exactly how the default paid subscription system works.
To set one up do the following:
- Goto "ACP -> Usergroups -> Add New Usergroup" and create a usergroup with the priveledges you want them to have.
- Goto "ACP -> Paid Subscriptions - Add New Subscription" and create the subscription, in the "Usergroup Options" select the usergroup you added as either the Primary or Additional group (your preference here)
So if a user subscribes to the paid sub you created when Paypal sends the success message back to your site (this is automated) the user will automatically be assigned to the usergroup.
If the user allows the sub to expire they will be removed from that group.
Job done.