Almost certainly, the communication path would be A ↔︎ switch ↔︎ B, not going through the firewall and router. Assuming that workstations A and B have IP addresses with the same network and netmask, they should be able to interact with no router involved, because the switch knows how to forward packets. You should be able to verify that there are no intermediate hops between A and B by running
traceroute ip_address_of_B from a command prompt on A. (On Windows, the command would be
tracert instead of
That said, alternative scenarios are possible, but less likely.
In the old days, before Ethernet switches were prevalent, there were Ethernet hubs. Hubs work the same way, except that they would unintelligently duplicate and forward incoming Ethernet packets out through every single port of the hub, instead of out of the appropriate port as a switch would. If you had a hub instead of a switch, then the router would see (and ignore) all traffic between A and B. Of course, such indiscriminate packet forwarding creates a lot of unnecessary traffic, and Ethernet hubs are uncommon these days.
Another possible (but unlikely) scenario is that the switch could be configured to do port isolation. That would force each workstation's traffic to go through the router. You might want to do that if you considered the workstations to be hostile to each other — for example, ports at a public library or in separate hotel rooms — and you don't want them to be able to directly communicate at all. In an office environment, though, it's very unlikely that your network administrator has set it up that way.
To answer your question in layman's terms: the network should naturally do the "right thing" in your case. However, it could be deliberately reconfigured to do a different "right thing". As a corollary to that, it could also be accidentally misconfigured to do a dumb thing.