Can I use Apple TV on a non-HD TV with HDMI connections?

Yes. The Apple TV box (any model) is compatible with any TV that has an HDMI-in port. It does expect a 16:9 screen, though.

Set up your Apple TV - Apple Support

If you get no image, then the current video settings on the Apple TV box may not be correct for the TV. Then try cycling video settings using the remote until you find a valid setting (step #5 from the link below).

If your Apple TV doesn't turn on or shows a black screen - Apple Support

Just to be clear if it is a non-HD TV and you are trying to use an adapter for the HDMI connection then that is not guaranteed. You also have to keep in mind that any commercial content will require HDCP so if there is anything in the chain that does not support it won't be able to play that content.