Yes, it's perfectly possible. Example sentence: The brilliant student had a very fashionable outfit on today.
I am fashionable.
That is a very fashionable hat!
"I love Kathryn's style, she's always very fashionable."
Jessica Simpson's shoes are quite fashionable.
A sense of anomie is blanketing the country
She is so intent on her ordeal that she walks like a somnambulist in a desert instead of a debutante in a fashionable crowd.
The adverbial form for fashionable is fashionably.
the adorable calico jacket was so fashionable at the mall.
The superlative of fashionable is "most fashionable."
They wore fashionable clothes.
Verbs do not usually describe things, they deal with activities. It is adjectives that describe things. Fashionable IS an adjective (as in fashionable cloths). On could also use an adverb (with the verb to dress) - fashionably dressed.