Jim,
In theory a constant current welder should work. But in practice, a welder is designed for far more current than is needed for anodizing. This makes it likely that the current regulation at the lower current levels is not very accurate.
For anodizing, there is a "Rule of 720". This states that it takes 720 amp-minutes / sq. ft. to build up .001" thickness of anodizing.
As an example, let's say you have a part that is 8" x 8" x 1/2". This has a surface area of 144 in^2 or 1 sq.ft. If you want to know how much current you need for an hour in the tank, its 720/60 you get 12 amps for a .001" thickness. If you want to go to two hours, it will only be 6 amps.
It is not recommended to use more than 12 amps / sq. ft.
The largest parts I have anodized were .55 sq. ft. yours may be different. To further put things in perspective, I used a 65 watt 19 volt LapTop power supply (I had lying around) and a cheap Constant Current controller I got on fleabay. It works great for the size of tanks (2 gal) that I am using. I am "upgrading" to an old 250 watt PC power supply....