I've been know to connect an outside scanner antenna to my handheld scanner with excellent results. I'll let the antenna gurus chimes in, but I think TV antennas/cables have a different impedance so there may be an signal reception effectiveness issue.
Right, a two way radio and a scanner are usually 50Ω impedance. A TV antenna fed by coaxial cable is usually 75Ω impedance. That won't hurt anything at all if you are receiving.
Even if you were to transmit, that impedance difference won't make that much a difference. Plenty of people use cable TV hardline (75Ω characteristic impedance) to transmit with.
The TV antenna is going to be horizontally polarized, while most of the stuff you'll want to listen to is going to be vertically polarized, and that will impact the strength of the received signal. If you were going to use the TV antenna -only- for your radio, you could rotate it 90º so the elements were pointing straight up and down.
Do keep in mind that TV antennas are traditionally directional, so they'll work better in one direction.
Don't transmit with this setup. While it's unlikely to harm the radio, some TV antennas have built in amplifiers in them (newer ones, not the old one) and transmitting through them might let the magic smoke out.
At any rate, I can't see an antenna regardless of type/style affecting the battery capacity.
Won't impact battery capacity on it's own. If it's picking up a lot more traffic, that will result in the receiver/audio amplifier working harder, which will run down the batteries a bit faster.