yeah--you would have no problem with the plot---except you should probably know that....in the first movie the princess was human and had a curse put on her that made her turn into an ogre at sundown. At the end of the first Shrek, the curse was supposedly broken and she was to turn into her true self--which ended up being an ogre (much to everyone's surprise).
Anyway, her parents in the 2nd movie are surprised to see her, because she no longer looks like their little girl. Shrek was the one who rescued her, and they fell in love. The donkey attached himself to Shrek because he had nowhere else to go--and they became a duo.
There....now you're all set for Shrek 2. Have fun!!!