Godaddy definitely does this, if not directly, they also can suggest the domain you've search to other people searching because it is likely a good domain...
It's the reason why I just use `whois domainiamsearching.com` from the command line whenever I look up domains I'm interested in. Way quicker than the web based look up, as well as not having to worry about some third party (or your isp) trying to snake a domain out from under you
For .com and .net names using the above method Verisign GRS has access to that info. There is nothing to prevent whois.verisign-grs.net (or the others they operate) from logging your request -or- from someone sniffing it by other means (it's plaintext after all).
Someone sniffing my line, while is of much greater concern, is also much less likely to occur. GoDaddy (or any other whois website frontend for that matter) automating registrations if a whois lookup purchase isn't made immediately is much more likely, purely on a practical level.
