joncnunn is correct to a certain extent. Default AI flavors would still apply, but AI grand strategies dynamically modify AI flavor. Brazil might still be among the more peaceful civs, but they will still get Conquest Grand Strategy's +2 leader offense flavor (or +1, I can't remember). The AI also only chooses a grand strategy about 20 or so turns into the game, so you would not observe any immediate effect.
Grand Strategies actually exert quite a substantial amount of control. For example, if the AI is running the Conquest Grand Strategy, they will always try to build a military force that is large enough to create an operation to attack another civilization, even if they are not running any operations (operations are how the AI handles large, coordinated attacks by a group of units, eg. sneak attacks or targeting a barbarian encampment). If the AI is running Culture Grand Strategy, they will always want at least two spies as diplomats, even if they don't have players to target with those diplomats and/or they would gain more by stealing techs to reach Internet faster. If the AI is running Diplomatic Grand Strategy, it will never attempt to conquer or tribute a CS, no matter their military score. Spaceship Grand Strategy gives a whopping -5 to leader religion flavor, so an AI running Spaceship Grand Strategy will pretty much ignore religion and faith generation, even if faith-purchasing Great Scientists, Great Engineers, and science buildings with Jesuit Education, as well as having happiness or % production beliefs are some of the best ways to set yourself up for a Spaceship victory (the only reason it isn't on Deity is because of the AI's massive boost to faith generation making it extremely difficult to make use of your own faith generation).
One thing to note is that the AI does not have support for partial Grand Strategies (at least not in the unmodded game): the AI is only ever running one of four Grand Strategies, and has no support for "these two grand strategies are both viable for me, so while the one is definitely my main one, I'm going to give the other one almost as much priority". This is primarily why you might see the AI erratically changing their behavior over the course of the game: two (or more) of their Grand Strategies are pretty much tied for importance, so they will swing whichever way the random roll that happens every 20 turns will go.