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.
The radio is only going to work as well as the antenna it has.
Installing a proper antenna will get the most out of your radio. Using an incorrect antenna is going to result in disappointing performance. Considering you probably spent a few hundred bucks on the radio, it would be a very good idea to follow up with a suitable antenna.
The OP is referring to a mount to hold the radio, not the antenna.
The scanner is not going to be hurt by the stray magnetism from a magnetic mount. Flash memory is not magnetic storage, so magnetic fields will not corrupt it or damage it unless you get into super-strong magnetic fields such as those found in a MRI machine.