So for now, I am manually dosing with 8.25% chlorine about half a gallon two days a week. I know that adding chlorine adds salt to my pool, and I eventually want to switch to a SWG. So I got to thinking about switching to a SWG without having to add any salt first. How long would I have to manually dose with chlorine to get my salt level at about 3800?

Using poolmath, it says if I add 80 oz. of 8.25% it will raise my FC by 3.5 and my salt by 5.8. (15000 gallon pool). I am assuming that is 5.8 ppm, so 3800 divided by 5.8 is 655 doses. I dose 2X per week, so that would be 328 weeks. Is my math correct? So that would be 6.3 years before my salt level is good?!?!

Acid (muriatic acid) adds chloride as well. It's going to take some time to build up the necessary chloride levels. Even heavy bleach users with pools running all year only get 1000ppm or so per year.

So that would be 6.3 years before my salt level is good?!?!
I didn't go behind and check your math but it would likely be longer than that. Splash-out and overflow from rain is a consideration so I think your math points out the ineffectiveness of that idea.

So I guess it's one of those things that is only good "in theory". I do dose about twice that amount during the summer time, but like you say, I have splash out and rain overflow will fight against me. I don't think that I can wait six years before switching to a SWG

Just be sure to check your salt levels BEFORE adding salt. Many people are often shocked that their chloride levels are already 1000ppm without ever having added salt. They think their salt levels are 0 and calculate their salt needs based on that which results in over salting. Also note that, when setting up your SWG, you should wait a minimum of 24hrs after adding salt before energizing the cell. Salt can take quite a bit of time to fully dissolve and evenly distribute throughout the pool volume.