... but does it scale?

Of course, this is not a question with an easy answer as your mileage may vary. But with the appropriate server-side configuration your WebSocket server can easily hold a lot of concurrent connections.

This is an example benchmark that was done on the smallest Digital Ocean droplet, that also had a couple of other Laravel projects running. On this specific server, the maximum number of concurrent connections ended up being ~15,000.

Here is another benchmark that was run on a 2GB Digital Ocean droplet with 2 CPUs. The maximum number of concurrent connections on this server setup is nearly 60,000.

Make sure to take a look at the Deployment Tips to find out how to improve your specific setup.