Probably not, We have first hand evidence from Silvano de Gennaro (the man who uploaded the photo) and this doesn't give an exact date:
Back in 1992, after their show at the CERN Hardronic Festival, my
colleague Tim Berners-Lee asked me for a few scanned photos of "the
CERN girls" to publish them on some sort of information system he had
just invented, called the "World Wide Web". I had only a vague idea of
what that was, but I scanned some photos on my Mac and FTPed them to
Tim's now famous "info.cern.ch". How was I to know that I was passing
an historical milestone, as the one above was the first picture of a
band ever to be clicked on in a web browser!"
In fact I've just found this quote in the page for the photo on wikipedia, it appears someone has already asked him directly:
When I asked him about a date for the picture's upload to the web I
got the following response:
"I don't think there is actually a date. I gave the photo to Reinard,
who was working with Tim in July '91. At the time the web was a
prototype, and only a few people were using it. Reinard and the others
played with that photo during the development of the software
interface to display photos. So it's been on and off the web for a few
months, until one day the GIF interface worked fine and the photo
stayed on the server and became accessible to the other surfers. I
don't know exactly what date that would be, and I doubt anyone does.
Another thing is that I believe that interface (XV) was originally
only developed for Unix. I know that because I helped develop a
similar one for VAX/VMS a few months later. Sorry but that like I
said, non of us knew we were making history..