If your thermostat requires electricity to operate, like most modern thermostats, you will need to connect a C-wire. If you leave it open, your system won't turn on, since the circuit won’t be complete. If you don’t have a C-wire system, there are remedies. Many manufacturers such as ecobee and Nest provide you with an extension kit that’ll let you power your thermostat externally. In addition, there are a few devices that are specifically made to bypass the C wire.