Yes, Solaris 11 has a GUI, but No, you can't use it via PuTTY and a serial connection.
You will need to be able to reach the machine via Ethernet. You will also need an X-Windows server on your PC. I don't know if PuTTY can do this (I don't use PuTTY). Maybe Google for 'Putty x-windows'.
Then, assuming you've installed the Solaris GUI software (look in [tt]/usr/openwin[/tt]), this should get you close...
[ol 1]
[li]Log into the T2000 via PuTTY as root[/li]
[li]Start your X-Windows server on your PC (yes, it's called a server, not a client)[/li]
[li]Via PuTTY, on the T2k, define where the display is to be sent. Use your PC's IP with this command '[tt]export DISPLAY=X.X.X.X:0.0[/tt]'[/li]
[li]Quick test with '[tt]/usr/openwin/bin/xclock[/tt]'. A clock from the T2k should pop up on your PC if everything is good.[/li]
[li]Start the GUI: [tt]/etc/init.d/dtlogin start[/tt][/li]
[/ol]
At this point, you should see some gui-ness trying to start on your PC. If not, look for error messages and dig in there.
Depending on your X-Windows server, you may also be able to have it launch the whole desktop for you, so you don't need to use PuTTY at all.