Can it be watched without seeing the previous part?

I'm sure it's a moot point by now for the OP but for anyone else with the same question:

If you've seen the first one but not the second then there will be certain characters (Vanessa) and experiences (why H&K are shocked that NPH is still around) that will be lost on you. For the most part the second movie focused more as a continuation of the first movie (it takes place directly after the original) so besides a couple of allusions or throwbacks to the second film there isn't anything that relies too heavily on seeing the sequel to enjoy the third film. Personally I felt the second film was the weakest out of the three but that's my opinion and there are a lot of people that will dispute that.

If you've seen neither of the films prior to this one then I would advise against it. This movie is based around characters that have changed somewhat drastically in the time-frame between the first and second films versus the third. This movie is more akin to a reunion and reconciliation versus a stand alone. On top of the elements you would miss from skipping the second film (mentioned above) you would also have no idea or interest in Rosenberg, Goldstein, NPH, or Maria. The entire NPH subplot can work as a stand-alone in each film but it works much better when it relies on the previous sub-plots. Amongst a number of other numerous allusions or nods that this film throws to fans of the previous fans a large part of the movie would be lost in trying to establish a connection with main and secondary characters that have radically changed from those in the original film. In short, you can afford to miss the second film (although I wouldn't recommend it) but trying to jump in without seeing either of the two prequels will make it a wasted experience.