I had a little dabble but there doesn't seem to be an "easy" way of doing it.
Doing it in Options is fairly easy using a named template and the "Array Sub-Options" field, like so:
Unchecking "Enable Page" automatically disabled the three nested elements, like this:
However, Style Properties don't use the same concept.
So although you can use a named template, there is no array sub-options field.
I suspect it may be possible doing a completely custom template using standard HTML and class="Disabler", but for what is essentially just a minor UI issue, I'm not sure it's worth it.
Perhaps that's why I can't find a single example of nested checkboxes in any of the SPs