Viewing figures yes, but not necessarily income. You've now got two broadcasters paying instead of one, and that will offset any drop in sponsorship money. Viewing figures will likely be very impressive for the first year at least whilst people try Sky out, and it may lead to a new audience that otherwise wouldn't watch the Beeb coverage. I agree that last bit is unlikely as I can't think for a second where they would come from, but F1 as a whole aren't in the habit of making losses.
F1 isn't a cheap sport, and by the very nature of it the fans tend to have spare cash (not all though, obviously). If they're passionate about the sport they'll more than likely shell out for Sky, so I'm not sure just how much of a drop it'll be. If it's about 50% it'll be a good deal.