How do I search for profiles online without logging into the game?
Solution 1:
You could use SC2Ranks (no longer a valid website) to find stats on individual players. On each player page is a link to their official profile page on Battle.net.
For example, my (sad) stats: Ewal
And near the upper left corner of that page is the link to my profile page: Ewal on Battle.net
Solution 2:
It seems like you cannot search for the profiles any more, but on the site
http://www.rankedftw.com/
You can search for the player name. There you see this ladder symbol: 
which leads to a stats page, which should give you an idea of the skills of that player