Sure, especially MI1 and Mi2 are basically from the very same creators as TWP (which doesn’t mean you have to stop after the second one 
).
TWP was born because of those past games and has gameplay an UI similar to Monkey Island, graphics are pimped up Maniac Mansion-style and controlling multiple characters is also from there (you won’t have that in MI), plus influences from a lot of other old games like Zak McKracken and the Alien Mindbenders.
Regarding Monkey Island 1 and 2:
Thanks to the Special Editions those two games are readily available again in a lot of stores (GOG, Steam and others). They are remastered versions with new graphics and voice overs (MI1 didn’t have voices 30 years ago…). But they also allow switching between old graphics+UI and new one which is a very neat feature.
There is one caveat with MI1:SE though: This one doesn’t allow playing with old graphics + voices enabled at the same time, at least not out of the box.
But if you especially like the old-school interface and graphics and still want voices you can modify the game by yourself (here is a quick overview on how to do it, just ask if there are any questions).