No. Largely because the holiday, hell, even the religion isn't about him in the first place. The staggering paradox of the myth of Jesus and the contradictory information about his life and death and the things he says or possibly said basically tell you everything you ever need to know. It is a study of our own inadequacies, failings and fears through the lens of something at least marginally easy to understand - the life of a guy who did things right. If there ever was a Jesus, you can bet he was just that.
And, for the record, regardless of one's feelings on the content of my above interpretation, that is not a condemnation of the religion. Because in the end there is strong evidence to suggest that Jesus wouldn't like the religion constructed around him if only because that construct entirely misses the point. Sure, people will point to the bit about "only getting to heaven through me" or some similar line but if ever there was an example of narrative dissonance, that's where you'd find it in the bible. To that end, I'd suspect Jesus wouldn't like us celebrating his birthday, especially when we are more or less told that isn't his birthday and the historical record tells us exactly why we celebrate on December 25.
As others have hinted at, this was because of the common pagan celebration of the Winter Solstice which on the modern calender is December 21st. That move was part of a larger process that introduced significant pagan messages and meaning into the religion that took place between the first and fifth centuries CE. If anyone would like to know more about that process, there was an incredibly tedious but fairly compact book on the subject called "Christianity and the Roman games" (There is a lengthy sub title) that offers a fairly comprehensive overview of the academic evidence based around the notion that Christianity was propagandized in contrast to the traditional view that Rome was Christianized.
I don't know where you'd find a hard copy of the book but it is available on various e-readers for a pittance.