Would it work? Yes.
Would it work well? Depends.
The big issue is that VHF and UHF frequencies (I'm guessing that's what you want to listen to) are generally line of sight. Putting antenna antenna like this up in your house isn't necessarily going to work any better than most other antennas. The key is you want your antenna to "see" the transmitting antenna. Stuff the antenna down inside a house, and it's not going to work as well as having an antenna outside and up high.
TV signals are traditionally transmitted with horizontal polarization. Land mobile radio (public safety, businesses, etc.) traditionally use vertical polarization. So while using a TV antenna is possible, it's going to suffer unless you mount it so it's vertically polarized.
I'll also say:
$89.99 for that is a rip off. There is usually just a "bowtie" shaped element in there with an amplifier. Inside your home, the amplifier may just amplify interference from TV's, computers, LED lighting, etc.
Ideally you want the antenna outside, up as high as you can safely get it, and in the clear.
If you have to use an indoor antenna, then get one that's designed for the frequencies you want to listen to. It'll be cheaper.