Will it help the tomatoes on the top to grow if you cut off the lower branches with no tomatoes?

Will it help the tomatoes on the top to grow if you cut off the lower branches with no tomatoes?
I know some tomato plants have what I call succer limbs that don’t bear tomatoes. I would like to get rid of these before my tomatoes start growing.
I started growing tomatoes for the first time this year. I have both plum and big boy tomatoes. The plums are ripening, but I notice that there is a hole (like it is rotted out) on the bottom of the ripening plum tomatoes. What can I do to prevent this from happening to all my [...]