Yes, with a close grip you really should be touching at the very bottom of your pecs. You still need to concentrate on pushing straight up.
I sleep on my side and have no shoulder problems. I should caveat that by saying I rarely have shoulder problems that bother me when I sleep. An injury will cause me a bit of sleeplessness. In which case I have an extra pillow that is by Tempur-Pedic that is very VERY firm and lifts my head way up taking any pressure off the shoulder in question.