It would if you used
Game Options. See the bottom of the page RicardoRix linked for the
User Preferences section. These are options you can set up that only affect the client side interface for each player. Example uses of User Preferences are Carcassonne, where players can choose to see the first edition tile graphics, and Stone Age, where each player can see the classic vs anniversary style meeples or the summer/winter side of the board. You can access these in-game by clicking on the hamburger menu in the upper right, or the "Options" tab below the play area.
In fact, the BGA framework already includes a built-in option to disable all tooltips, so you don't need to create a separate preference for it, unless you would like to only disable
some of the tooltips.
Unfortunately, not many players at BGA know about User Preferences, but they are a great way to handle situations like this.