Will he get us promoted with this squad? Probably not, there are too many areas where we're glaringly short of consistent quality. But then I have no idea who we're going to sign over the next seven and a bit months to fix those issues. I think Weimann is a decent start.
Is it fair enough to have concerns about whether he can ultimately take us up, full stop? Of course, he's only ever promoted one team from this level. He hasn't immediately come in and propelled us to promotion style form. He isn't someone like a McCarthy, Bruce, Allardyce or Warnock who at various stages proved that if you gave them the budget, they'd probably do the business, whatever you thought about their style or them personally. He could emulate his Norwich work, he could end up being an average Championship manager and that was all just a perfect storm down in East Anglia, it's happened with many others before (Dowie, Brown, Megson, Jewell, Coyle, Holloway etc etc). Worth remembering though that your own choice in Rowett - as much as I rate him - has 0 promotions from this division, not even a playoff finish...
However - when you're questioning whether he has improved us then it is not a matter of opinion, it is a matter of facts. He has improved us, the evidence is there, I've posted it on the last page. You are of course entitled to your own opinion, you (or indeed anyone) aren't entitled to your own facts.