Yes. No. Maybe. It depends.
First, a browser may use any of these strategies for connections:
- Single connection (unlikely for any browser more recent than 1995)
- One connection per tab (basically same as #1, just very slightly better)
- One connection per resource (naive, but doesn't work so bad)
- Pool of connections with keep-alive, re-using connections
- Something different (read as: weird stuff)
You don't have a way of knowing which strategy a browser will use, although using a pool of connections (and re-using connections) is a reasonable assumption.
Second, the way TCP works, you have a source port, and a destination port for every connection. The pair of source and destination address/port defines the connection.
You always use a well-known port (such as 80 or 443) to connect to the server (to which it listens on its advertized address), but the other port is randomly chosen. Thus, depending on from which side you look at a connection, it either has one or many possible ports.
Thus, the same tab may (and usually will) use several different ports on its end, but in principle different tabs might (if connections are pooled and different resources in different tabs are loaded from the same server) use the same port.
Since the question explicitly mentions outgoing, in the "normal" case, the port numbers would be the same regardless which tab they're in, or one of two possible ports (80 and 443). Although of course it is possible to explicitly ask for a different port (like 8080) in an URL. That's kind of rare, though.
Well, not always
... but let's not complicate it too much.