Yes. You just need to run
export DISPLAY=:0 (or whatever the remote display is numbered as) in your ssh session and programs run will run on the remote display. A quick example:
oli@bert:~$ ssh tim
oli@tim:~$ export DISPLAY=:0
Firefox is now running on
However when you close your ssh session, most of the time the remote application will close. If you want to disconnect from ssh but leave the application running you need to launch it in a special way using something like screen (keeps the ssh session running in the background) or
nohup, or another method. For more information on this there was recently another question on it.
You can shorten this all down into one command that will connect, export the display in-line and start the application in a way that won't close it after the ssh session dies:
ssh tim "DISPLAY=:0 nohup firefox"