Connect a channel drain to existing drainpipe

I want to add a channel drain at the front of my lean-to in order to direct rainwater from the lean-to's drainpipe into the existing house drainpipe. I understand that this is not a typical usage situation for a channel drain, but I can't see why this wouldn't work?

This is the channel drain I am thinking of buying:

And this is how I am thinking of connecting the two drains:
#Drain #Drainage
Drain Drainage