Another issue you have to deal with is the user perspective. The user perspective is a kind of usability from the user point of view and - in this case - simply means: "How much effort do I need to invest to run this game?". Far too often this question is silently ignored by newcomers, thus it is brought up here. If a user first has to install dependency X for the GUI you have integrated, then has to get and install the GUI and then can run the game, it is possibly too late (unless your game has outstanding concept/graphics/gameplay). He simply will remove it from his computer.
You therefore should check if the GUI library you are about to integrate in your game can be incorporated in your game distribution or if it has many third party dependencies, for which the integration/installation effort is higher than the benefit.
p>First of all, pygame relies on the SDL, which means that it can only have one window at a time. Thus, trying to implement multiple Gtk, Qt, ... application instances that use pygame, is an impossibility. The second problematic reason is that those toolkits use their own main loop, which possibly forces you to pipe their events to your pygame instance and vice versa. And to mention some other points in short: Drawing the toolkit elements on the pygame window is impossible and the SDL/pygame fullscreen mode will be problematic.
As you see, using those toolkits together with pygame will, in nearly any case, cause more problems than their usage solves. So let's quickly go to the next section.