A car antenna WILL work!! I have used them before to keep from letting folks know I have a scanner in a car. Might not get everything but I picked up all I needed to hear.All it is is a piece if metal which is just about MOSY scanner antennas are anyways.
I have used fixed length AM/FM car antenna for scanner reception and it worked fine.
It is true that they are generally at length for 88-108 mz, but since various multiples of higher range frequencies are contained within that length, you will find generally pretty good reception on 140-170 mz VHF, 420-512 UHF, and even 700 - 800mz.
If your antenna is sectioned extendable, you can tune it better to the band you listen to.
The most important thing it does is get the antenna outside the metal frame of the car.
As mentioned above, they used to make Y adapters that would split your car antenna input to go to the radio and another unit. You then would need another adapter to go from that connector to either BNC or SMA, whichever your scanner requires.
It's a very cheap solution, and does not advertise that you have electronics worth stealing in the car.
Like wtp says, try it. I would say it depends on what you want to listen to. If, like reedeb says, what you desire to hear is fairly strong, some sort of trunked or repeater system, or not afar, it should fit the bill.
The same goes with listening to FM broadcast. Instead of getting a splitter, see if you can receive the FM stations you want with a foot or so of wire on the dash or in the rear window. I once used the car antenna for scanning, and a 6" NMO antenna mounted inside a rear window for FM (didn't get AM well, but I never listened to AM anyway) and it got the FM stations I wanted full quieting.
"Old style" car radios that were stand-alone items that you could remove from the car as a lump and run it on your test bench just used a telescopic antenna of no specific length, a length of coaxial cable and a Motorola plug - the coaxial cable capacitance was actually part of the RF amplifier in the radio and you could 'tune' the cable for best reception on AM. On VHF FM the antenna was a pretty good length to be a quarter- wave and so worked quite well.
Then came the cars that had the radio installation built-in to the dash panel and were integrated into the vehicle wiring. Often the antenna was either very small on the rear roof or in the back window - quite inefficient so they concealed an amplifier somewhere down the back to bump up and match the signal - works well. The plug on the back of the radio has a terminal for the antenna which also supplies voltage for the amplifier - not the Motorola style connector at all and no need for tuning the cable as it's already 'tuned' at the amplifier.
So a fender mounter telescopic antenna with a motorola plug is nothing special - it's an untuned bit of metal - it will work well as a 2m ham band antenna if in need - I made an adapter Motorola to UHF for the purpose and it worked given a bit of shading to the rear!
So as many have said - suck it and see! There's no reason why a normal car antenna shouldn't work as a scanner antenna, how well remains to be seen. I have no experience with the adaptor/splitter, you may lose more than you gain. There's probably not much more than a couple of capacitors in the box - you'll probably have to retune the trimmer in the car radio after installation IF your car radio is has one of those - if your radio installation already has a concealed antenna and amplifier - forget it!
I have tried this over the years, with success ranging from very good to lousy and most of everything in between. Give it a try if you want, adapters are cheap, and who knows, you may just be pleasantly surprised. I found switching the AM/FM co-ax out for RG-58 or RG-6 was helpful, if you were willing to sacrifice your broadcast reception. Most people won't want to take it that far though.