Yes Allegri can bring Milan back to winning Serie A and for good reason. He is highly experienced coach who has already won Serie A title with Milan in 2010-11 and then dominated with Juventus winning five consecutive league titles. His success comes from his adaptable tactics and along with his skill at managing players and adapting to different opponents all of which Milan needs for consistent top performance. While Milan has shown flashes of brilliance they have lacked consistency and your hope for Allegri to provide leadership and mental toughness for them to finally win Serie A title next season is reasonable one given his proven ability to build winning teams.
Experience alone is not enough to bring a team to become a champion. Allegri needs to get support from management to make player purchases that Allegri needs. Many names of players are rumored to be Milan targets, but until now there has been no deal, except Modric just almost coming to Milan. If management does not immediately make a decision to support to buying player as Allegri expects, then it will be difficult for Milan to be better next season. Maybe they are just made a target for UCL, not to be a champion.