Yes the big ones will. The small ones I leave in their containers or ground and cover with a bit of leaf mould or similar and they just grow the next year. Mrs B
I didn't know that, Mrs B.
You're the Begonia expert here, and helped us get all ours going, so when you write a book about them, I'll buy a copy as long as you sign it!
Mrs Growster overwinters all our geraniums in the GH, as the following year, they come out well in advance of any new annuals we might buy, and give a splash of colour after the daffs etc have died down!
But this year has been fabulous for begonias, and we'll do better next year! They seem to like all this rain too...