Short answer, yes you can.
Long answer, depends what you are trying to do.
To get the transmission out is not extremely hard. You will want a transmission jack to support it. I got mine at Harbor Freight. Transfer case comes off first. Support the transmission with the jack, remove the cross member and let the tail end sag down. Remove the shift linkage and wiring. You will have to rotate the engine to get to the flexplate to torque converter bolts. You will need an offset wrench to get these bolts out. Standard wrench won't work and not enough room for a ratchet and shallow socket. Once it has sagged down, you should be able to see all the bellhousing bolts. I recommend about 24" of ratchet extensions to get to the bolts on the top of the bellhousing from the rear. The cooler lines are last. They have a quick connect that has a retaining clip that is almost impossible to get out. I just unscrew the quick connect fitting from the housing. At this point you should be able to slide it rearward. Vent lines slide off last. NOTE. Once the trans is on the trans jack there is not enough clearance to slide it out from under the truck. You will need to jack a corner to be able to roll it out from under the frame rail.
Now on to the next question. If you are looking to just replace the transmission, not any 4L60e will do. See my rant in my build thread. Forget about buying a 2wd trans. The output shaft is the very first part that goes into the case. In order to swap it out to a 4wd output shaft, all the trans internals need to come out. The second thing to look for is the input shaft and bellhousing. The I5 bellhousing is specific to the atlas engines, it's not standard chevy pattern. All the later 4L60 have removable bellhousings. You can swap that rather easily. This requires a special torx bit to remove the bolts that is a special order. You can't find it at Lowes or Home Depot or even Sears. You also need to make sure the input shaft is the type that supports the 245mm converter. If you have the wrong input shaft, the trans has to come partially apart to change it out, plus sourcing the parts, etc. If all this is correct, the pan, valve body, 1-2 accumulator and spacer plate all need to get swapped from your original trans to be able to clear the front driveshaft. If you pull the valve body, its crazy not to spend the few bucks on the paper gaskets that go with it.
I rebuilt mine, mostly because once I got into it, I wasn't sure what combo of parts I was going to need to make things work. With my swap, I needed the front end to look like something off of an LT based v8, the bottom end to have the H3 compatible parts. You can order generic rebuild kits for under $400 that include all the seals, soft parts, clutches and steels. If you go that far, another $100 will get you a few nice upgrades for longevity. The rebuild takes a few specialized tools for compressing some springs, but I MacGuyvered some of it and made it work without buying anything. The torque converter should be changed and should be a shelf item.
Here are my recommendations in order knowing what I know now.
1. Purchase used/rebuilt H3 trans and NEW torque converter. Will be a long one day project start to finish to pull old trans and install new one. Will need to invest in a tranny jack and maybe some hand tools (offset wrenches and ratchet extensions)
2. Same as #1 but carry it to a shop and spend $300 labor and let them mess with it and drive away clean and happy. Take the time you save and have a beer and watch some football.
3.Pull your transmission and carry it down to a rebuild shop and have it rebuilt. I would say $700-1100 range depending on shop. You will save the labor of pulling it and reinstalling it. For the money you save doing this, you may not get a warranty with the trans.
4. Bite the bullet and have a shop do a full rebuild on your transmission. Cost $1400-$2000 depending on shop. Shop around for reputation and best warranty
5. Find a good used/rebuilt 4WD with the correct input shaft configuration. You will need to swap valve body, pan and a few lower parts. This is likely the lowest out of pocket $$ option, but you could encounter a pitfall or two so be prepared.
6.Rebuild your own trans. Should be able to do it for under $600 with new torque converter. What is your time worth? Make sure to do plenty of research.
The big thing with any rebuild or cracking one open is the penalty for not having it right the first time. If something doesn't work, you are looking at another day of labor just to get it down to find the problem and reinstall the whole mess. Don't forget this includes pulling driveshafts and transfer case each time. I spent about $800 on my initial build including a $100 core donor for the right case, input shaft and bellhousing that I needed for my conversion. Once I had the right fluid fill, I think everything was right in the build. 2 weeks later, problems arose that I think ultimately was valve body bolts vibrating out. But I ended up pulling the whole thing down and rebuilding the pump again not really knowing at the time. A second failure happened when the torque converter solenoid also vibrated out, which burnt the torque converter clutch. I pulled it again and changed the torque converter during the summer. This partially fixed the problem and I eventually burnt it up wheeling from a combination of low fluid fill and high trans temps (my own fault). When I ultimately broke down on the interstate in TX, I was forced to have it rebuilt. The shop charged me a more than fair price of $1400. Picked it up 2 days later and haven't thought much about it since.
In the end, its all up to you what your time is worth vs the potential cash savings.