Okay, the best info I've found on Whites is here:
Tons of pics, manuals, serial numbers.
And here:
Treadle On with info on Whites, including removing the "head" of the machine and changing out the handwheel to convert to treadle (not as easy as Singer).
I think the Whites are plentiful and fairly easy to work on, but there's not as much info as for Singers. I believe they also made machines that were badged. So, some of the Kenmores, etc. will be White sewing machines. Some of the parts can be more difficult to find, like the "t-shirt" shaped bobbin coverplate, but they can be found.
One other thing to note, if they were electric machines, they were friction drive, so no belt. Converting one of those to treadle looks more difficult than with the Singer machines because of the way the handwheel was made. I'm going to attempt to do this at some point, but I haven't done it before.