As mentioned in one of the comments, if the fluid is incompressible (i.e. - has constant density) then the absolute level of the pressure will not affect the drag.
However if the fluid is a gas, then the pressure and density will be strongly related (directly proportional for ideal gases). And the density of the fluid enters into the equation for the dynamic pressure, so it does affect the drag.
For a constant drag coefficient, the drag will be directly proportional to the density, so for streamlined shapes at sufficiently large Reynolds' numbers, the drag will be approximately proportional to the pressure.
This should be true even if the Mach number of the flow is small enough for the incompressible flow equations to be used.