@goldfish In my experience, unlikeable characters lead to people disliking the player behind them.
If the character is just a dick, some players might not feel they have the energy or not be interested in an antagonistic or rivalry based relationship IC. If the character commits immoral acts, there are even players that will call you, the player, gross, and avoid you. It doesn't matter if your character believes they are doing the right thing, or if the character is just an actual unrepentant monster; there are folks in the hobby that will take it as a reflection of your character. That's why I personally gravitate more towards white hats these days, and I think that's why a lot of MU players tend to gravitate towards white hats.
If you can find a good group of players that you trust, and have a solid OOC rapport with, or that you feel have the requisite sort of maturity, though, I think you can totally make a very unlikeable character.
I think as you said, competency doesn't much matter. As long as you are secure in your incompetence, you can show up to a big fight scene with your firearms 0 character and enjoy yourself.
Activity is another matter. I think it depends on the game and the kinds of plots that intrigue you? But, that said, its easy to make a character that is, conceptually, the sort that folks go to for help under rare or specific circumstances, the kind that only reaches out to help once in a blue moon, and isnt in the public view for very long. A hermit, a reclusive black market arms dealer, a mysterious homeless man with a lot of battle scars and an encyclopedic knowledge of the city's history - more so than four professors of history put together could offer - these are the sorts of characters that can weather periods of inactivity or absence and still have a lasting, interesting impact on a story.