We should come to an agreement on what "greenhouse effect" means.
In my opinion it means two conditions must be met:
1) the outside part of the system must include materials that are rather more translucent to shorter wavelength, light and rather more opaque to longer wavelength light.
2) the system must have light shined on it.
According to my definition, there is certainly a greenhouse effect on mars. I think that if you could wave a magic wand and change all the CO2 in mars' atmosphere into N2, that mars would cool a little. Though I would be very surprised if it would be by a significant amount.