Yes, there is access for drop-off on both sides. Not sure exactly what you mean by "drop-off", however. If you want a convenient place to park and say goodby, I'm not sure that would be easy. I don't go to that area by car, so never really looked for parking.
But for just a quick drop-off, either side works. The SouthEast side (Wynkoop St) gives you a direct access into the main hall of the station, the restaurants/bars and AmTrak. From the NorthWest side (Wewatta St) there is a convenient escalator and underground walkway through the bus station and then another escalator up to the main hall. Very passenger and luggage friendly.