I had to wait 8 months to announce my first deal, but that had nothing to do with finding an illustrator since I was the illustrator too. It just took that long for them to send the contract and we weren't allowed to announce until it was signed. My recent sale we announced after about a month. (But we still don't have the contract)
So yeah, there's no hard and fast rule. I know of people who waited a really long time to get to announce for a variety of reasons. I don't think it always takes a long time to find an illustrator, but sometimes it can take a really long time before an illustrator is free to work on the project.