Web server accessing the database server in Always on availability group
Now my question is if my network team only allows only the Always on availability group listener port will that be a problem

You can configure an AG Listener to use whatever port you want, and you can configure your application to connect using a non-standard port.

what if the network team dont allow access to that port

A &quot;normal&quot; DMZ has external access to hosts in the DMZ and limited access from the DMZ to the internal network.  If the network team won't allow connectivity from the web server to the databse server, you can put the database server in the DMZ or use a cloud hoster instead of a DMZ.
For instance you can use Azure App Service for hosting, and use Azure App Services Hybrid Connections for secure access to on-prem resources