NO, providing a C connection provides an alternating current return or common path.

R = 24V hot
C = 24V common or return or neutral
W = call for heat

I have installed many HW wifi systems that do not use any batteries and are powered from the furnace (need to have a C connection). Memory is still retained with a power loss even without a battery.

Nest uses a battery for all of its power and operations. The C connection allows the battery to charge at all times instead of using power stealing technology to charge the battery.

My personal opinion is still to do as you said and get a different thermostat. Nest is a good thermostat and has its place in the market. Its just not top of the line or a professional thermostat, IMO.