If you have an inferiority complex, you will work hard to compensate for your perceived lack of quality. However it's not always the case that people work hard have an inferiority complex.
Also for the record, Rooney has worked less and less hard as he's become more established. That's nothing to do with Rooney. All players do it. All teams do for that matter, Barca don't press nearly as well anymore because they started to believe their own hype.
Did ICIP get banned for this?
Whilst I'm not entirely sure of the logic in terms of whether it applies to Welbeck (he could just be nervous about other matters whilst trying hard to cement a place), whether 'inferiority complex' is the correct term or if we can even say for sure what's going on, there is a general topic to be talked about amongst any assumptions at least. We often praise players for working hard, but 'working hard' itself in certain instances may stem from a pressure to appease the crowd, or from nervousness or a lack of ability. There are obvious exceptions, but someone like Darren Fletcher may be a good example. I was quite young when I watched him play outside of the first team, but I don't remember him charging about like a mentalist (like the 08/09 Fletcher) when he was better than everyone else of his age group or when he just started coming on to the scene. It started happening at some point during the 06/07 season, and I'm guessing that's when he thought that he might have to do something to combat the pressure from the crowd and the jeopardy his future was in.
Personally, I think Welbeck has a higher level of ability than he's showing, although it could just as easily be down to other fears, insecurities and defficiencies as it could regarding his own ability. I've always felt for a youngster it must be quite daunting going into the first team and playing with first team players who will be all too willing to get under your skin if you're not performing, so perhaps there is some of this with Welbeck. I'm guessing not everyone would react well to playing with Wayne Rooney, for example, just as I'm sure not absolutely everyone played to their best around Keane despite him being known as a quality leader. There was a marked improvement in several players almost immediately as Keane left (Ronaldo, O'Shea, Ferdinand and Fletcher, for example), although you could just as easily argue that it was a natural progression.
I think this sort of thing is probably a lot more prevalent than we'd assume in football, and has almost as much of an impact on a player's progression at the top level as actual ability.