Oh you bet it makes a difference. I can totally tell a difference in production if the birds have been socked in with a week of rain versus great sunny days (albeit not super hot).
A couple days ago I only got 2 eggs. Yesterday I got 4. And today I got 6 eggs, which is the most ever from my 10 pullets. So I know that at least 6 of them have started laying eggs. A couple days of non-rain, made a big difference, even though we have not had any sunny days for over a week.