Yes, our Splashtop Remote products do, in general, support connection via 4G. However, the latest Splashtop Remote Desktop HD for Android, version v220.127.116.11, has a known issue on the Samsung Galaxy Tab 10.1 tablet with Verizon 4G in the United States.
According to our own tests, we found that the Google Talk service is not stable over the Verizon 4G network. The current workaround for this is to manually configure Port Forwarding on the home router.
Please take a look at this article for how to do ports forwarding: http://support-remote.splashtop.com/entries/514213-how-do-i-connect... (Requires some technical know-how...)
If YOU are also having problems with 4G connection, but you have a different situation (not the Samsung Galaxy Tab + Verizon situation mentioned above), then please let us know about it by entering a Comment below, and describe your case in detail.
Update: According to our user feedbacks, our app can work very well on AT&T LTE service. (20/12/2011)