It won't hurt if it's just the antenna connected to the scanner. Make sure there isn't any amplifier in line with it.
Since the antenna is designed for 700-800MHz as well as 1900 and up into the 2GHz range, it's going to work best on those frequencies. You'll find some public safety traffic in the 700-800MHz band.
Since a lot of radio traffic is also down in the VHF and UHF bands,where these types of antennas are not designed to work, it'll be a very poor performer there.
Ideally you want an antenna that is designed for the frequencies you plan on listening too.