Most likely, yes, Big Bang Theory, as a fictional television show, exists in the Arrowverse.
On the show, Cisco often makes pop culture references to television shows, movies, etc. that really exist. He particularly likes to name-drop "geek" shows, and Big Bang Theory likes to pretend that it's a show that geeks like. His fellow Earth-1 geeks typically recognize his references, while the Earth-2 people often don't. This implies that Earth-1 has many of the same TV shows we do.
Note that Cisco has also worn a number of shirts from Adventure Time and at least one that I believe was a Doctor Who reference, so it would be entirely in character for him to wear The Big Bang Theory shirts as well.
On a side-note: I doubt that Sheldon's shirt is meant to be a reference to Flash in the CW, though I suppose it's possible. Sheldon wears geek shirts all the time, and The Flash is a pretty well-known DC comics character. It may actually be a reference to the older Flash TV show, as that would be completely in-character for Sheldon.