I don't think it is. On my previous iPhone 6 Plus, I did plug my IMEI into one (or maybe several) of those sites to get more information about my phone. I only used sites recommended by users on various forums I visited.
I was just visiting https://supportprofile.apple.com (since it was mentioned early in this thread). Looking at the entry for my former iPhone 6 Plus, I noticed not one, but two instances of submitted cases entitled "Cannot lock or unlock phone." I did not submit those!
I can't help but wonder if giving an IMEI to these sites is related to the current problem of phones being activation locked to a strange email address as soon as the current owner has released them from "Find my iPhone." (See https://www.macrumors.com/2016/10/05/iphone-activation-lock-wrong-apple-id-issues/ )
For my new iPhone 7 Plus, I plan to keep my IMEI and serial number a secret between me, Apple, and my carrier.
