That's not a fair yes or no question. I can't confidently say yes, he is; neither can I say no, he definitely isn't.
What I would say is I think we're close to a side who can do that and I've seen a few signs recently which give me hope that yes, we will under Wenger over the next few years:

We have started to make more major signings, like Ozil and Sanchez.
We have a better squad than we've had for years.
We won a major trophy last season.
We've won a couple of big away games this season, the sorts of games which we traditionally lose or even get hammered in.
One of those away games was in a Cup Quarter Final - again, the exact sort of game in which we've repeatedly failed. So now we're in a semi-final against a team I believe we'll beat. We could yet retain the FA Cup.


Now. I also recognise that we've had plenty of false dawns previously, but some of the above haven't happened for us for a while. If we do win two cups in two years then it won't have been a bad couple of seasons, despite some of the frustrations. I agree with you that the Chelsea game is significant in terms of beating a Mourinho side. If we do that, finish in the top 3 and win the Cup would it have been such an awful season? Would a manager who achieved that really deserve the ridiculous level of abuse you mete out?

As a club, we need to move on from Wenger if only because of his age. I personally don't think there's any big hurry to do that though.
While the billionaires are allowed to run amok I can't see us dominating like we did in the early noughties under any manager, but I do think we're well placed to challege over the next few years. There may be managers out there who would be better placed to do that for us but I don't think there are many.