If you are following ASME section IX guidelines, it depends on how your weld procedures are tested and written. Our foundry made a wide variety of steel, stainless steel and nickel base grades and poured castings from a few pounds up to 3000lbs. Everything was heat treated before weld repair. All of our weld procedures were written to the rules of ASME section IX. For the carbon and alloy steels if your PWHT was above the transformation temperature of the steel, the qualified thickness of weld repair was limited by your test coupon thickness. However, by keeping the PWHT below the transformation temperature the weld thickness was qualified for up to 8". Also, most filler metals are not designed to be normalized or quench and tempered. I did need to make a procedure for WCC with a normalize for the PWHT so a 70S-6 wire should still get you the tensile for A-27 but if you are needing to repair 80 or 90ksi A148 grade parts I don't know that your normal wire is going to get you there. More highly hardenable A148 grade materials do not like to be welded in the green condition.
You also need to think about how parts move through your foundry. Our foundry and cleaning room were separate. Green parts never left the foundry/heat treat facility. So in the cleaning room we did not need to keep track of what was green and what was heat treated. If you clean, inspect and weld in the green condition, the parts will still need to come back for final inspection and occasionally additional welding after heat treatment. You need a mechanism that can differentiate between green and heat treated parts. That can get complicated depending on your heat code system. Our heat code for standard parts was based on the part number and master heat. So we would have a number of the same part numbers with the same heat code. Having two parts with the same identification in the cleaning room, one green and the other heat treated would be a concern. Having a green part shipped to the customer would be bad.
So, you can weld green parts, depending on how your weld procedures are written, the steel grade and how your foundry controls parts. I don't know that I would recommend it.
Bob