Is it possible to use telnet to connect to remote computers/hosts using only a WiFi connection and no direct connection to the modem except through the router?
It should be. If you are using Windows 7 or Vista, however, you need to enable it first.
Start > Control Panel > Programs And Features > Turn Windows features on or off
The telnet options are in there. Tick the ones you need, and apply the changes. A quick test is the ASCII animation of starwars, of coure.
In command prompt, use 'telnet towel.blinkenlights.nl'. If it works, then telnet was successfully enabled.
As far as Telnet is concerned, wireless vs wired networks are identical. As long as the machine you want to telnet to is running the telnet server and the ports are open on the entire route between your client machine and the server then it should work fine.
If you're using a home router and trying to connect to it from outside that network then you may need to configure the router to open that port and send connections for that port to the server.
You can install
telnet command (as suggested) by using the following DISM command:
dism /online /Enable-Feature /FeatureName:TelnetClient
Then test your connection like:
telnet example.com 80
example.com is your destination host (like your gateway IP or can be
localhost for local PC) and
80 is the port number.
When you connect, to disconnect, hit Control+], then type
quit command to exit.