Sure, I don't see why not.
But you have to remember that any cable adds some attenuation. The amount of attenuation depends on the type of cable and the length. Also take note of the fact that the cable should have the right impedance (50 ohm).
This means that you should not just cut the cable and solder something in between. Always create a proper antenna cable with connectors and place this between antenna an board.
The type of cable used for the pigtail (the small cable between the board and the antenna) is RG174. This cable has about 1 dB attenuation per meter, RG58 only 0.5 dB and Aircell 7 even just 0.2 dB.
So if you add 1 meter of RG174 cable, you could have 5m Aircell 7 with the same attenuation.
Adding a long cable to get your signal from the ground floor to the roof might even give you a worse signal than with the antenne next to the window ... Always use a good quality cable with good quality connectors.
See http://www.hamshop.nl/coax-kabels.html or http://antennekabel.nl/antenne-kabel-1.htm for the stuff you need