Yes, you can. There is a non-steam counter-strike.
With it, you can play on any public non-steam server and there are a lot of this kind. You can download cs from here
http://69.90.34.115:82/counter-strike.zip
Unpack and play.
Thou I'm not sure of a non-steam server where you would have low ping.
Here are some servers I usually play at.
69.90.34.115:27015
69.90.34.115:27016
69.90.34.119:27015
If you want to try and find some, try
http://www.game-monitor.com/
There, in "Playing" put Counter-strike, in "within" something like 1000km and in "Server with" type no-steam or non steam so it could find every server near you which support non steam players. And usually there are a lot of this kind.=D
