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It is not just about flow it is about sewer gases and building codes.Not a plumber. But maybe you can tap into the top of the 2". Reason I say top is that I don't think your 2" pipe is ever really "full" of water. I would put a drain saddle clamp at the top of the 2" and see if water runs out. If it doesn't then you're good to go. I'd also consider a check valve on the RO waste line.
There has to be drains in a basement. Usually by your furnace at minimum to deal with the condensation involved.I've looked. No floor drains. Just a bunch of those 2" drains coming from upstairs into 1 giant pipe going outside.

