Not really.

The way a service works is that it listens on that port for a connection request, then scurries that connection over to a temporary port for the life of that connection. For example, with SSH (port 22), the server will receive a connection request from the client, then move that connection over to a bank of ports for this process (ex 49153). Until that session is disconnected, that port is dedicated to your connection.

When it comes to web servers, the communications are in short bursts, so this port reassignment is done very quickly.

(See https://en.m.wikipedia.org/wiki/Ephemeral_port for more info.)