There is no requirement for how much you play. If you do have a lot of logins with very quick logins, there's a decent chance that at some point you may get pulled aside to ask what's going on. I would rather not be too specific, but based on what you're describing, I wouldn't be particularly worried. Just keep in mind not to be logging one character out, then quickly logging in another.

Generally, if your character isn't one that -other- characters aren't being impeded by your lack of playtimes, no-one's particularly concerned. Scion in general is rather tight on players, and alt characters will be frowned upon. Otherwise, I would say only things like cabal leadership and Empire Elite Sect Members (restricted #s of these) are going to be particularly concerned.

Beyond that, the major downside you'll run into with things such as cabal promotions, empowerment, or tattoos is that with lower playtimes your chances of interacting with those who you might need to go down as well. I would say I feel Imms generally make a particular effort to check on empowerment characters. Beyond that, there's nothing directly against it, though I think there is some human nature that the character who is around all the time will more likely get the attention than the one rarely seen, but that is generally out-shined by a well-played character.