I've done a lot of those but I've never gotten a single rejection. But I also don't use the ICANN site he recommends because it puts a cap on how many times you can search for a domain. Instead, I use WHOIS.COM because it gives you the same information without forcing you to fill in captchas or stopping you from searching if you've done too many searches already.
Also remember on the Administrator form, he's looking for the website administrator, not the registration information with the domain. It's separate and often hidden by privacy services like Domains By Proxy, so you'll see Admin Name: PRIVACY INC. and Admin Email:
329083249iasdf@domainsbyproxy.com. I always include those in the post to show him I looked up the info.