The 4L80E will not run without a computer, period. But there is good news... I'll get to it in a minute.
The 6.2/6.5 family of engines was designed to basically bolt in place of any chevy engine, so the SBC swap should be a super easy breeze. Just confirm that the motor mounts are the same (or buy the proper mounts) and drop it in place. The bellhousing bolt patterns are the same. Two things you'll want to consider; 1) the diesel typically uses the large bolt pattern on the torque converter, so you'll probably need the larger (168-tooth) flexplate on the SBC. and 2) the diesel torque converter is a low-stall unit that won't be optimized for a gas engine. It will physically work, but it might seem a little sluggish off the line. For that reason you might want to get a stall that is properly matched to your 350
The good news I promised... Hotrodders for years have tried to find cheap easy ways of gettting a 4L80E to work in their old cars. One of the ways they have discovered is to use the computer from a 6.5 diesel. It has to be modified internally somehow, but do a search on some diesel forums and you'll find that the diesel PCM is one of the ways to get a 4L80E to work behind an old-school engine. I don't know the details, but someone in the tranny forum might.
But... I'll say it again, because I know your next question is going to be, "can't I just shift it manually?" or "how can I get it to work without the computer?" You can't. Period. The only thing you can do is install a race-type manual valve body along with some other modifications and then shift it manually.