Yes. The hard part is getting its handle, as there are different "handles" structures for each GUI. If it has a unique name, you can use findall('Tag', 'TheAppropriateTag') to get its handle.
Once you have its handle, you need to fake the callback. See http://www.mathworks.com/matlabcentral/answers/275495-press-button-automatically-click#answer_215068 for more information.
But easier than all of this is to have the callback in GUI_1 call a function which has its own .m file, and then when you want the push button in GUI_2 to invoke the action, have GUI_2 call that same routine.
