The CCV does not cause increased oil consumption over time. If it is full of condensate (the white paste) and it then freezes, it can either freeze in the open or closed position. In one of those, with high vacuum conditions such as on overrun, the CCV can draw oil out of the sump into the intake, creating large clouds of blue smoke. In the other scenario, the crankcase can be pressurized and then oil will be pushed out the weakest point, usually a valve cover gasket. So both can lead to oil loss, but both are drastic, not something that results in the loss of a quart over hundreds of miles.

If the CCV has frozen, you will know it as the vehicle isn't driveable.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue