Can you enter Doha with VISA on arrival on your passport?
If yes, then you won't have any issues, as even in the worst case scenario where they don't let you go through transit and make you exit and re-enter.
Where it might possibly get a bit trickier is on the way back in ATH as usually the agents will ask for your QID (Qatar ID aka your residence VISA) if they see a ticket for DOH with no ongoing destination. Which should be easily overcome when you show them the other ticket with the DOH-SEA leg.
I have a US passport, so I don’t think a visa is necessary for me to enter Qatar for such a short amount of time. But like you mentioned, hopefully just showing the onward ticket prevents the conversation altogether.