It will do something alright. Most likely it will be for the worse. When you do something like that then you are changing the impedance of the circuit that is your antenna/feedline/whatever. Your scanner's rx input is 50 Ohm, works most efficiently when it matches to a 50 Ohm load (your antenna/feedline). Let's take two cases:
1) Dual adapter with two handheld rubber duck style antennas: This will probably put your impedance (z) somewhere around 90-100 Ohms. This will work ok for rx, but it is hardly as efficient as a matched system where all of the received signal is coupled to the scanner.
2) Dual adapter with a rubber duck and an external antenna via a random length of 50 Ohm feedline: The best way I explain this setup is to use an analogy of ghosting on your cable TV picture. Ghosting occurs because there is a compromise in the cable line somewhere and your TV is receiving the same signal at two slightly moments in time. The audio is not as affected by ghosting, but it can still have an effect. The signal through the rubber duck will reach your scanner much quicker than the signal coming from the external antenna and through your feedline. This is because of the cable's velocity factor (VF), which is anywhere from 65%-95% that of free space. So, say your coax has a VF of 75%; that means the same signal going to the rubber duck will reach the scanner 25% faster than the signal coming from the external antenna. Just like on your TV, your scanner signal will have some ghosting now. There are some other factors, but that is basically it. You may not notice these effects on a FM analog signal, but I bet that digital control channels and such would be affected, which could result in a poorer scanning experience.
Now, with that said, there is another rub to case #2. You can do some magic with calculated lengths of coax to make stubs that will show a z of 0 Ohms. This is similar to the way that multiband HF antennas are constructed, and, to a lesser extent, multiband VHF/UHF antennas. The basic idea is to have a length of the coax or antenna that "disappears" at certain frequencies. Let me know if you want more info on that stuff, it's a lot to type and I don't want to get off topic here.
Jeff