Well, politically, it’s basically replacing one main prop for the monarchy with another. The Tyrells would definitely be looking to replace Lannister appointees with their own people. On the other hand, they’re better at PR and making alliances and sharing the wealth, so there’s going to be less resentment.
Personally? Margaery would definitely be a lot better at managing Robert, because she’s better at performing than Cersei ever was. Robert would probably be besotted and over-the-top-generous in that class mid-life-crisis second-marriage way, although he’s probably still going to drink too much and sleep around eventually. Very much likely to do that Henry VIII I’m still young thing – big question there is whether Margaery can get him to whip himself back into shape or whether she’ll have to fake being in love with OldElvis Robert.
Something to consider here is how Robert becoming aware of the twincest will affect Robert emotionally. Will this make him suspicious of Margaery at all times? Would he lock Margaery away in the Maidenvault to ensure that she can only get pregnant from him? Would he be inclined to mistreat or distrust Loras? This could piss of Margaey and Loras and the Tyrells.
Maybe, but if Henry VIII is any model to go by, I don’t think so. Rather, I think he’ll salve his ego by pointing to Cersei’s “unnatural lusts” as proof that she was always the problem in his marriage not him, and putting Margaery on a pedestal as the superior, properly feminine, woman who’s proof of his continued virility.
Especially since Margaery would make it her business to be fun to be around – witty and vivacious, endlessly flattering, coming up with entertainments to keep him interested, and so on. If anything, I think Robert would be more clingy than suspicious, wanting Margaery around him constantly to show off to other people, to have her ooh and awww at his accomplishments, and to share in the merriment.
As for Loras, from the book, he seems more inclined to treat him like the son he never had. And if he started to get suspicious, all it takes is a word in the ear about Loras and Renly to allay all suspicions.