No, the birds will sort the bedding out - but what I do is rake some thatch and moss out of the lawn, put it in a wire netting 'ball', or just in a piece of garden netting, and tie it to the fence - the birds come and help themselves. If you have access to some sheep's fleece (gleaned from hedgrows, not from the sheep's back 
) or combings from the coat of a long-haired dog or cat, you can do the same with that
It's a little bit late to put bird boxes up - the best time is early winter so they can suss each one out - but you may be lucky - it often takes a couple of years for birds to use a new box.
Fix it just above human head height in a sheltered position where midday sun won't overheat the box, and where there's a clear flight path to the opening. Oh, and out of the reach of cats!
