Someone, somewhere, has probably done it, but there's a lot more that can go wrong than right, and it would probably not be ultra cheap. You'd want to use PE pipe, not PEX. Design has several rules of thumb, but there's a lot more than two thumbs there. Oversize the pump, your electrictiy consumption skyrockets. Undersize it, and you won't be effective. Same goes for loop sizing. Also, groundwater table plays a huge part in thermal conductivity, and seasonal variations can be considerable.
I'm an engineer, who does pretty much everything myself (concept>design>build), and I considered DIY geothermal for our HVAC unit. I designed it, priced it, would have done all of the installation myself, and had a engineer/contractor bid it to check my work and price, but in the end it was too expensive and too many variables.
Ymmv.
If Farmer John pops in and says yes, he had a spare radiator and did it for super cheap, and it works great, I'll say great for him, and I'll be curious as to what he did specifically.
But IMHO, I wouldn't recommend it, you may end up wasting some pex, pvc, a truck radiator, ditch witch rental, and time.