The dictionaries seem to indicate so, but its not clear how the word is really used.
Also, is the word about person's art abilities, or taste in art?
Edit: Is it an internet slang, or general English slang?
The word does have some pejorative cast to it. It is not internet slang; it predates the widespread adoption of the internet (I remember it from ~1980s).
The word exists in contrast to the word "artistic". It often means, when applied to a person, that they have the personal style associated with artists: it suggests that they present themselves -- in speech, dress, habit, activity -- as belonging to a subculture of artists. In an important sense, it functions like calling someone a goth or punk rock or emo: you're saying something of how they seem to you, in terms of subcultural style affiliation.
Perhaps a better definition is that artsy means in the style of artists, where it is understood that there is some artists' style being alluded to. It is in the very differentiation between actually being an artist, and (merely) adopting the style of artists, that the pejorative implication arises.
Yes, it is a common English slang term and could be mildly pejorative. See here, where it is described as "enthusiastic about [art], though it may also describe someone who is pretentious".