Does Alkaline work with proxies and firewalls?

Yes it does.

Firewall settings are automatic in any network, so you don't need to worry when you want to query a remote server behind a firewall. You can specify the proxy setting in both the global.cnf and asearch.cnf files and use multiple proxies for different configurations. Alkaline supports HTTP proxies on any ports which is of course configurable.

You can run Alkaline on any port behind a firewall like any other standard web server.