The work depending on how close you live to the stations. Depends how high your dish is mounted.
Probably a good test to see if this antenna would work for you. Your rabbit ears work much better sitting on the dish than in the house. Some one in a metal walled building that lived 5 to 10 miles from a strong UHF that had trouble indoors this would probably be enough to pull in a signal.
If you live 10 miles from a weak VHF probably won't work.
There are two advantage to this antenna. One is it gets the antenna outside and if that is higher than your inside antenna the better.
The second advantage has nothing to do with reception. Some of them come with diplexers and a jumpers, so you just combine your satellite and
OTA into one cable, then split it inside.
Warning too. Since they are mainly designed to work in strong signal areas and have an amp built in powered by the sat receiver I assume (can't find any other way they would be powered), they would overload easy. Remember rule one of amps, they don't like strong signals.
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A much better approach would be to buy a j-pole attachment
Similar to this concept
Winegard DS 2000 Universal 22" Pipe / Tower Mount for Off-Air Antenna (DS-2000) | DS-2000 [Winegard]
Note the antenna shown is not part of the package. But a way to attach a small
OTA to a dish mount.
Of if they let you mount a dish, on a j-pipe wall mount, it's just as cheap to buy a second j-pipe for
OTA. And there are many small antennas that are end mounted that can be used.