If the widget inventory in the app remains stable/fixed (i.e. you are not creating lots of new widgets as part of the user interaction), and you're always just (re)using the same variable storage for data content being displayed in the widgets (e.g. "-textvariable" attributes for Label and Entry widgets, the same array for Listbox widgets, etc), it should run indefinitely with an unchanging memory footprint.

But as zentara says, you just have to test it out (and as most monks know, zentara is, hands-down, the top authority here on all things Tk).