Yes, but not all of it. The amount will drop to the vapor pressure of water at that temperature.
So let's do a thought experiment. At room temp (~72F ~22C) the vapor pressure of water is ~20 torr, so at 50% Relative Humidity the partial pressure of water vapor is 10 torr. We compress that from 14.7 psi (1 atm, 760 torr) to 120 psi, or increase the pressure by a factor of 8X.
In our compressed gas now the partial pressure of water should be 8 x 10 torr or 80 torr, but this may be higher than the vapor pressure of water so what is in excess of the vapor pressure will condense to liquid. At about 47C (~117F) is where the vapor pressure exceeds 80 torr. So if the compressed gas is cooler than 117F water will condense.
I don't know how much the compressed air heats up as its compressed (my calculation of adiabatic heat rise was quite a bit, but it is not an adiabatic system), nor do I know the efficiency of an intercooler (especially an air/air heat exchanger), but if we make the supposition that we can get the compressed air down to 90 F (32C) where the vapor pressure of water is about 36 torr. About 44 torr/80 torr or about 55% of the water will condense and hopefully be removed by the filter, meaning 45% will remain. So this 36 torr of water vapor is now in your tank. It will continue cooling with time to get to room temperature where the vapor pressure is about 20 torr. About 16 torr of the water will condense and end up in the bottom of your tank. For my 25 gallon tank on my compressor that would translate into about 1.5 mL of water(granted it is a bit less than the 5.5 mL from the 60 torr without the intercooler and filter), but it will still accumulate.
I am a physical chemist who teaches Thermodynamics, a Chemical Engineer probably could get a little better estimate than my back of envelope.(heat exchanger efficiencies and filter efficiencies and all that)
John (who sort of thinks there might be an exam question here for next Fall
)