Of course you can, you have plenty of ways to do it. Do you call a function/script in App Designer code or what?
Set a tag, or a unique name for your app in Component Browser, under UIFigure - Identifiers, and get its handle this way:
app = get(findall(0, 'Tag', 'AppUIFigure'), 'RunningAppInstance');
Now you have app in your workspace as well, you can assign values to app objects/properties
app.EditField.Value = Variable;