Egyptian troops spent most of the 1960s in Yemen, trying to prop up the military coup. 10,000 Egyptians died there, massive amounts of money were spent, and it became known as "Egypt's Vietnam." And while they were willing to send some airstrikes and move a couple of destroyers to pay back the Saudis for all the money they're giving them, it's unlikely they're going to do more.
4/15 is not a month ago.
I don't see the Saudis bringing in the National Guard as backing off.