On the day pun, yes it definitely is. Japanese twitter is full of these in November because it's month 11.
Don't mind the lack of the phonetic い in 11/23=いい兄さん. They have to stretch a bit to get those puns working for most of the days.
Like how 11/11 is supposed to be "pocky day" because it looks like 4 pockys side-by-side. Or how good married couple day is 11/22=いい夫婦 despite phonetically the number representation lacking an う too.