Hi jgbrunn! Welcome to the forums!
Personal opinion: Yes, I warmly recommend playing them in order. That way, you will understand the story better. Besides, Curse of Monkey Island is absolutely superb from an artistic and musical point of view. And the story is awesome. And the voice work. And the...well, just play it
And for all the tiny cool references, it's totally worth it to play MI3 and MI4.
If you don't have the patience for it, at least watch some "Let's Play" on youtube.