Sometimes yes, sometimes no. The thing about webisodes is that they bring the term "shoestring budget" to a whole new level. In the past, filmakers at the very least needed to drum up the money to make copies of their films for distribution-- now they just need to stay below YouTube's bandwidth and length requirements.
If you're watching a web series and you want to know if they have a corporate sponsor, they will probably flat-out say "Thanks to blah blah corporation for being our sponsor" (like in the old timey days of radio and television). If there's no such message, then you can safely assume that they're paying out of pocket.
If you're a content producer who is looking for funding? Your best bet is to create something on a shoestring first, and THEN hope it goes viral. If your idea is awesome, you'll have sponsors just like "Where the Hell is Matt?" (sponsored by Stride Gum) or Eepybird (sponsored by Coca-Cola, Mentos, ABC Family and OfficeMax).