HVAV no C terminal but available wires
No, because the G terminal gets power from the R. When you turn on the fan on ther thermostat, the thermostat is really just connecting the R to the G terminal.

Internally on the furnace control board, the other side of the relay that actually powers the fan is connected to C. R and C come from the two sides of a 24V AC transformer.

There's almost always a way to get C from any control board, it's just a matter of identifying a C wire from a schematic, or by finding the transformer and identifying how it's wired in.