Depends on the hoax. I worked in the media for a while and hung out with many media types for many years (discovering the true meaning of boredom). If the hoax is damaging to religion it appears on page one before it’s discovered to be a hoax and when discovered to be a hoax it appears (if at all) months later on page 8. The fairly recent “Brother of Jesus Found” incident (implying that Mary was not a perpetual virgin) comes to mind. If the hoax is perpetrated by a priest or religious individual/community, the order is reversed.
IMHO, if the tears were found not to be blood it would have been ballyhood immediately which leads me to believe that something’s going on. The Church too is reticent about proclaiming/publicizing “miracles” with good reason.
That said, even if the tears have been found to be blood it can, as you say, still be a hoax and great caution is needed. I’ll wait for the official Church decision if any, which might take years, decades or more…but I can have my own opinion!