Yes they do, though I've only had issues with the lowest trusses particularly if they are touching the ground. the skin seems to be torn and odd bits of it might be sticking up.
Birds also can be a problem (here sparrows and blackbirds seem to be the culprits) you can see the tell tale beak marks they make as they peck the flesh, looks like little stab marks. But obviously their poo is quite different!
Slugs or is it snails, kind of slime off slices, having rounded edges to the holes which are usually very shallow (at least to start).
Tomato Moth caterpillars can do a lot of damage to both leaves and fruits and often the way to find them is by the trail of copious amounts of poo they excrete!
Mice and birds go for ripe fruit, slugs usually ripe but sometimes unripe fruit and Tomato moth ripe or unripe.
Good luck finding the culprit.