Let's say I have set the hotspot and the web-proxy on MT. Web-proxy logs are redirected to a remote linux server. The question is; will visits on the hotspot's alogin.html page be logged into web-proxy logs? The idea is to count user visits on this page every month.

web-proxy logs doesn't log visits on alogin.html
see hotspot logs, you will be able to find something that you can count.