It depends entirely on the deposit bonus in question. Some welcome bonus offers (ones that refer to the first deposit) allow you to play wherever you like, at live dealer games or regular table games. These types of first deposit offers are intentionally designed to give new players a chance to test out the online casinos that offer them as freely as possible.
On the other hand, some recurring offers (that is to say, for returning customers) might only be focused on the live casino site. For example, you might get a deposit bonus for only a few live casino games, like live blackjack or live roulette. While the first deposit bonus is given to just get the players accustomed to the casino, subsequent bonuses could be used to steer them towards different parts of it - like the live casino, for example.