Can I hook up my 4K Apple TV to my regular smart tv?

setup boxes like appletvs bypass anything smart about your tv it input everything it is into the hdmi port and your tv is treated as a monitor with speakers. it can be as dumb as a doornail and any features it has is obvious to the appletv

As stated above it will work, however you will not gain any of the benefits of the 4K model without a 4K TV.