Is a signed Thomas Gainsborough Blue Boy print worth anything?

Most likely...go to The Blue Boy - Wikipedia..(google it) and read the history. There may be clues in this article..

I think if your referring to the lithograph of Blue Boy and it is a little over three feet tall by about two feet wide it was worth over a thousands dollars many year ago. Go to the ADA Antique Dealers web site adadealers.com and look under members section to find a dealer who works in these for a current price.