To answer your questions, Yes, it will work.
No, it will not work well enough to be useful.The A-coil and blower in your wood heat system is designed to distribute air at about 120 degrees to heat the shop. The forumula for heat delivery (or removal) via forced air is: Q = 1.08 * L * (tout - tin) Where Q is heat flow in BTU per hour and L is air flow in cubic feet per minute. A typical good sized wood furnace heat system might deliver 80000 BTU per hour. With the shop at 65 degrees you'd need a 1340 CFM blower. Best case, you might get 60 to 65 degree air out of your heat exchanger if you supply it with enough 50 degree water from the ground (you can't, due to the water flow capacity limitations of the coil and one inch pipe for that matter). With the shop at 75 degrees, you'd get maybe 14000 BTU per
hour of cooling capacity from 1340 CFM or 65 degree air. This is about the same as an ordinary window mount air conditioner. Why not just buy and install one of those if that's all the capacity you need -- it'll be cheaper than digging the ditch and burying the pipe. Real geothermal systems use a phase-change refrigeration cycle to pump heat "uphill" into (say) 75 degree circulating ground water. They can achieve about a 50 degree outgoing air temperature. With 1340 CFM of 50 degree air you'd get 36000 BTU per hour of cooling, or about 2.5 window air conditioners. A single 1 inch poly line is the wrong way to do a ground heat exchanger. You want multiple loops of 3/4 inch poly (to keep the loop velocity in the turbulent flow region), and a bigger header (to manage the required total flow without excessive pumping losses). You'd need about 1800 feet of 3/4 inch thin-wall poly for a 36000 BTU per hour ground source heat pump. Probably split it into 4 separate loops of 450 feet each. If you are cheap, and not using methanol, you can substitute thin-wall plastic poly pipe for the special geothermal underground tubing normally used. You sacrifice quality control and risk leaks developing over time but the thermal performance is equivalent. PVC is a horrible choice for geothermal transfer. The thermal resistance is much higher than polyethylene, and the walls are thicker. You need about 4 or 5 times as much linear footage for the same amount of ground transfer. (I use a ground source heat pump to heat and cool my house. I designed the system back in 2003, so I've forgotten some of the details..)
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