Vincent's appearance in P3P is non-canon, due entirely to two main things: 1. the timing of Catherine's plot and 2. Vincent's motivations for going to Japan (or lack thereof). The first issue is the main sticking point, since the entirety of Catherine's storyline takes place on dates that are different than his appearances in P3P. This wouldn't necessarily be a problem if his P3P appearance didn't indicate he was already in the midst of dealing with his life's troubles, but P3P pegs his cameo at early March in that game, whereas Catherine takes place over a week-ish during April. Given that he only exists in P3P as a means of virally promoting Catherine to those who bought the game, it's safe to say he has no real connection to the Persona series or, as other people have pointed out, Shin Megami Tensei games in general. While Teddie does show up in a few easter eggs, that's more of the game being meta or anything. If you wanted to theorize about a weird connection between Catherine and Persona through that tangent, then Persona is just another video game in the world of Catherine that's happened to get merchandising, although I really, really doubt you're supposed to think that deeply about it.
As for the whole Japan thing, the game makes it pretty clear that he's not living in Japan. The apartment and sushi place are weird discrepancies, but perhaps Vincent just lives in a major Asian district where that sort of architecture and culture would be more "authentically prominent," if you will. That's really the only justification I can come up with other than the team having a minor slip up or just wanting to make the game world a little bit weird. Also, Vincent's existing commitments both to his job and his relationships keep him firmly rooted in where he lives for the duration of the game. As an IT guy, he has no reason in particular to just drop by to Japan, especially just to get drunk. Those who are also still unsure that the game takes place in America or at least a Western country should note that the entirety of the cast has Western given names and surnames. Unless Vincent happens to be living in some weird foreign expat community, it's a lot more likely that finding such a concentration of Western names is just due to the fact that they're outside Japan. The scenery in general in the game also confirms that the game doesn't take place in Japan. I haven't spent the longest amount of time living in Japan, but I know it well enough to tell you that most of the country doesn't look like Catherine's world at all. Even the sushi bar is pretty westernized based on the layout and pieces of the scenery; if you look hard enough, you'll find things like credit card logos hanging around that indicate the place would take those as payment, something which you definitely couldn't count on having happen in a cash-centric place like Japan.
@Driadon: There's no overarching narrative as far as I know, although 3 and 4 have always had at least tenuous connections to the previous games based on some of the imagery employed, as well as the presence of Igor. The fact that you save your game in 4 by largely talking to butterflies is thought to remind series veterans of Philemon, an extremely critical character in the earlier games who otherwise makes no appearances whatsoever during the PS2 generation. He would often take the form of a butterfly when talking to players and developing the plot. 3 also employs the butterfly imagery in a few scenes, but to a less obvious extent than 4. Ultimately, people tend to interpret the butterfly thing as Philemon still watching over the casts of 3 and 4, arguably still giving at least some of the characters their Personas, since that was also one of his functions in 1 and 2.
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