| Not without sacrificing its function.
Usually there is a 24 volt AC transformer in the furnace with the secondary winding connected to a red wire running to the thermostat and a blue wire, common, to the gas valve, A/C relay, and fan relay. From the thermostat there will be white wire to the gas valve, yellow to the A/C, and green to the fan. The thermostat is wired to switch the power from the red to the white, yellow, and green as needed with the blue completing the circuit. Most thermostats and furnaces have the contacts labeled R, B or C, W, Y, and G for the corresponding wire colors. It may be wired to have the A/C control wires return to the furnace and its controls and then a second wire goes to the A/C unit. Internal wiring may replace the green wire if the thermostat does not give you the option of fan only or continuous fan. Digital or programmable thermostats may need the blue wire connected to them.
If you don't connect the transformer to the common, you may be having to change batteries all the time and losing any program. If you don't have an unused blue or other wire, you could connect the green or yellow to B or C at both ends, losing the fan on or A/C options. If you have a crawl space or unfinished basement under the thermostat, it may not be too bad of a job to fish in another wire. | 
Linear Mode
