It shouldn’t mess with your current routing but if you’re running other VPNs you may run into issues.
After you join the machines to the tailnet, each machine gets a new IP address ( only visible to other machines in the tailnet), by default it’s a 100.x.y.z you can check the tailnet for the device IP.
Now you can keep the port closed on your router and it will still be accessible over the usual lan ip and port. But when you want to access remotely, turn on tailscale and connect using the tailnet IP.
Another cool thing you can do with this setup is turn your home server into an exit node. By default it will only route things that are in the tailnet (100.x.y.z subnet). But if you turn your home server into an exit node you can funnel all your traffic back through the exit node. Instant free VPN back home!
Can you tell me more?