There's no single "signal", there are packets. On Ethernet, packets (frames, if someone insists) are either addressed to a single device (unicast), or to all of them (broadcast). It's the broadcasts that you'll be having most problems with.
(For simplicity's sake I'll count multicasts as broadcasts, because the switch probably doesn't do IGMP anyway.)
Some things will conflict
Most data traffic would not cause a problem. It's unicast, it goes from port A to port B, all other ports will just ignore it. Is it recommended? No, but you can get away with it.
Unicast traffic is bootstrapped using a broadcast ARP query – that might cause some unexpected troubles, although generally hosts will just ignore queries not meant for them anyway.
But you have the issue of multiple DHCP servers on the same ethernet – one from your ISP for the WAN side, and one from your router for the LAN side, both sharing a broadcast domain. As a result, devices might keep choosing the wrong one.
LAN computers will generally pick the DHCP offer that arrives fastest – which is usually from your router, but by luck only. Sometimes they might accidentally pick up a WAN address.
But the router will also pick the DHCP offer that arrives fastest – its own. The DHCP queries that it sends to the WAN port will simply loop back to the LAN where the router itself will respond. Chances are it'll never get an Internet connection this way.
How to make this possible
Use a switch with VLAN support (a universal feature across managed switches). This will let you assign individual ports to different broadcast domains, completely isolated from each other.
For example, ports 1–2 can be moved to VLAN #2 for modem-router communication, while all remaining ports stay in VLAN #1 for your regular LAN usage.
(Tagging is not needed in this scenario.)
If the router uses PPPoE to talk with the ISP, that'll have a much smaller chance of conflicts. While PPPoE uses a very similar process to DHCP, most LANs generally don't have a PPPoE server randomly sitting there, so the only PPPoE Active Discovery Offer you'll receive will be the legitimate one from the ISP.