HTTPS SSH Tunnel
Yes, it is possible:
ssh -L 8443:serverA:443 -Nf [user@]<serverB>
This will let you point your desktop browser at port 8443 and send it to port 443 (the HTTPS port) on your server A. The -Nf will background the session and exit immediately back to your desktop, not establishing an actual shell session to server B.
You dont even require SSH Tunneling to access the web service in Server A. You can use Dynamic Port Forwarding
ssh -N -D 9000 user@server_b
and configure your web browser to use SOCKS proxy host 127.0.0.1 and port 9000