Yes, it is possible. The ideal case would be if it was visible from your home so that you can leave a tripod stationary and just attach the camera when you need to. If the construction site is somewhere else, however, you can't use the tripod to mark a location. Better try to think of a good location to shoot from with something that won't move for a while - e.g. a road sign, a traffic light, a post box, a hydrant or something else. From there, choose an appropriate focal length (taking into account that at first you'll only see the foundations but the building will grow tall) and framing (maybe using the camera's focus points in the viewfinder to "mark" something in the frame). Then proceed to actually shoot once or several times a day (depending on how much stuff is happening to the construction site). Photoshop can do a relatively good job at aligning consecutive frames (even shooting from a tripod will cause several pixels' worth of deflection); worst case scenario you will have to do some aligning by hand (but not aligning the images perfectly might not be that bad since the exposures will also differ).
Before everything, you may look around the construction site for a sign - it should describe the project, how long it should take and so on - to give you an estimation of how much time you have.