Nah....
I mean, im sure you have a blown head gasket, but that wouldnt cause your problem
A lot of times with DSMs (like mine) when the HG goes it doesnt burn coolant, but it pushes it out. The system pressurizes under boost (or whenever, depending on how bad it is) and it gets pushed out the overflow. Empty the overflow and let the car warm up, then do a few pulls. If the overflow is full, then its a HG.