Can the downspout from a gutter run inside a house?

[WashAsDelicates]

My house is L-shaped and I'm thinking about a single-storey extension which would fill the space inside the L. I also want to put a downspout from the two-storey roof in that internal corner. Could it be incorporated into the new building and boxed-in once indoors?

Why wouldn't you redirect the guttering down pipe to incorporate the run off from the room of the extension that fills the gap?

Does that make sense?

Yes, perfect sense!

Couldn't see the wood for the trees.