Nope, waste of money. That machine is 10 years old and very much "obsolete" in Apple's eye and should be yours as well.
You don't want to spend ANY money on a Mac that is greater than 2-3 years old. Spending $500 for that machine might seem like a good idea, but if the logicboard fails, it'll cost you easily $800+ to get it fixed. It's a HDD which will fail, so replacing with a SSD will run you another $250-300 for a 1TB drive.
Since screen size is important to you, Apple's Refurb store has
this 27" iMac for $1529. Yes it's $1000 more than the eBay model, but this is a 2020 model refurbished by Apple (trust no one else, I don't care what they say). You will get the opportunity to buy 3 years of AppleCare from date of purchase, so you'll be covered until 2025. Being a newer machine, it'll easily last you 10+ years without issues.
Old machine - $500 + $800 (for possible LB failure) + $300 (for SSD upgrade) and you're at $1600.
Oh and I don't trust eBay, so there's that too.