How do I search for profiles online without logging into the game?

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

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