In a word, no. There are no Star Trek novels that focus wholly, or even in large part on the life of an ordinary citizen of the Federation on Earth.
As I mentioned in a comment, there are, however, some stories about ordinary (alien) people set in the Star Trek universe, in particular:
The Never-ending Sacrifice covers the everyday lives of Cardassian citizens, starting during the Occupation and extending beyond the end of the Dominion War.
The Rihannsu novels address what life is like in the Romulan Empire, starting with the flight from Vulcan and into the TOS era.
The Vulcan Academy Murders have quite a lot of background about Vulcan during the TOS era.
But there isn't (as far as I'm aware) a comparable one for Earth.