test for overlapping axis labels

Can anyone think of a way to test if axis labels (breaks) in an arbitrary ggplot are overlapping?

My plan is to run such test and to decrease the font size until there is no more overlapping.

I just stumbled over ggplots axis guide which allows to check for overlaps and remove axis labels if there is overlapping. This function may be suitable to get a return value which indicates overlapping yes/no but I could not figure out if this is possible.
Also, comparing axis-labels of a ggplot-objects with or without check.overlaps by axis guide may be an option but how exactly?