Italian managers seem to have a pretty decent record in the Premier League.
Mancini, Conte, Ranieri, Ancelotti all league winners...and Allegri's pedigree is certainly decent.
https://www.bbc.com/sport/football/45582990
As for the football, can't be more dire than it is now
Well I wrote a decent post about him a while back
Good points about Allegri
a- He's got plenty of experience in dealing with a flawed owner. If you think the Glazers are bad then you haven't heard about Berlusconi. Imagine a scenario were one of the Glazers suddenly thinks that he's Sir Alex Ferguson but doesn't bother taking the job himself for fear of having to sack himself out of it. That is Berlusconi in his latter years at Milan.
b- Unlike LVG/Mou, Allegri doesn't have a philosophy. He builds his strategy by speaking his players, learn their strengths and weaknesses and build the team around him. In fact his formations changed regularly throughout the years. The guy isn't afraid to play players out of position either. He's the master of versatility.
c- No one organise a defence better then he does.
d- He's a superb man manager. One of the best in the job on that.
e- His teams nearly always punch above their weight. Cagliari, Sassuolo, AC Milan (until they sold him everyone). Conte ridiculed Juventus with his you can't eat in a 100 euro restaurant for 10 euros jab (to justify his poor record in the CL). Allegri came in and nearly won the treble
f- I (and half of those watching Italian tv at the time) had a crush at his girlfriend when she was young.
g- He's a genuinely nice guy. He will joke around players, in interviews etc. However don't try and piss him off though. The guy held his ground against both Sacchi and Adani. If Gaz comes with crap on him he'll answer back
Bad points about Allegri
a- he would always prefer workrate & attitude over technique.
b- because of A, he tends to play the older players. Kids might showboat something Allegri doesn't like
c- That doesn't mean that he doesn't rate kids. He does rate them. Unlike Conte who couldn't bother knowing their name and used to just call them 'boys', Allegri cares about the young generation. Just don't expect him to build around 17 year olds. He won't
Conclusion
Allegri is not LVG or Mourinho. Rather then a rigid manager who thinks that everything rotates around his brilliance, Allegr is more like the Mcgyver of football who would scavenge around trying to sort his problems with the limited resources he's got. That what he did at Milan, Cagliari, Sassuolo etc were he had to punch over his weight with the limited resources given. Having said that, this usually result into a team built around players who are hard working and have great attitude. That doesn't mean he's scared of superstars. He did well with the likes of Ibra, Pogba and Ronaldo as well.
Can he cover Sir Alex job? I very much doubt it. There again no one can. These days managers rely on DOFs and great football CEOs as much as a human being rely on oxygen to breathe. Allegri had worked with Paratici/Marotta whom I think are among the best in the job. However, if we get Allegri we will get a solid manager, whose a great man manager and whose extremely versatile in terms of tactics. On that regard he's the closest manager we've had to Sir Alex since this very day. In many ways he does remind me of Sir Alex during his last years.