A bit more informed answer, from a few sample texts found around the internet the language seems to my layman eyes an awful lot similar to Creole spoken by the people of Cape Verde.
It almost seems like a phonetics based language, where most words are written as they are pronounced, as if one was spelling them phonetically, with a certain degree of distortion or 'accent'.
There also seem to be a considerable degree of Spanish influence added to the mix.
There are lots of similarities, some words are close enough to be understood, but my guess is that if a native Portuguese speaker were to listen to someone speaking fluent Papiamento, it would probably be hard to keep up and completely understand a full sentence.
Judging from say Creole, which probably share a similar etymology, there are some similarities between certain words, but they some times differ enough in pronunciation, to make it dificult to understand immediately in regular speech.
With some repetition or time to process one might piece together enough information to understand general concepts or meaning of a sentence. Same goes for written text.
So I would say no, they are not mutually intelligible. This of course is a bit of a subjective matter, and people with a more 'flexible hearing' or more used to foreign languages may find it easier to interpret Papiamento.