Yes that is possible as your VPN client sets up a network interface like any other interface, and it sends and receives packets all the same. If you start a server application that listens on all available interfaces it will also listen for incoming connections on that VPN interface.
But just like your other interfaces you should have a firewall in place that blocks or ignores all incoming connection requests (except for the ones you have configured to be let in).
On the other end of the VPN connection (the VPN provider’s side) the system would normally also be firewalled and configured to not accept any connection requests going your way as that is not the service they are intending to offer and would also be a rather obvious security issue. The VPN services you have in mind are setup for one way connection requests, you can use it to connect and communicate by starting from your side, but not the other way around.
Other VPN setups like office-to-office interconnects would be configured differently, allowing connections both ways. But that does not apply in your case.
As long as you treat your VPN like any other internet connection to the outside word and filter/firewall it accordingly you will be fine, connection-wise.
There is one risk: the VPN provider itself. There is nothing preventing them from changing the settings on their side and have a bunch of traffic thrown your way which your firewall then has to block (so best keep it enabled). So the real question to ask yourself ends up being: how much do you trust them (and why).