It is possible, there is a guy at my local track that runs a SBC in a fox body. You will need a custom K-member, either fabricate one or purchase one from Jegs. They make one that will work with a SBC.
http://www.jegs.com/i/Anthony%20Jone...-3030/10002/-1
As for headers, most guys used the S10/SBC engine swap headers. You will need a custom driveshaft, transmission crossmember, and small stuff like radiator hoses that will fit the 350.
Not to mention, when you get everything installed and get it running, that 350 will probably destroy the 7.5" differential in your '84.
If you are adding these costs up, it is easy to see that it isn't "cheap" compared to Ford parts. For a street car, I don't think you could do it and break even with the additonal costs. If you were building a 10 second drag car, the cost savings of the chevy drivetrain would probably overshadow the swap costs.