The AA lathes that Sears sold came with one or the other of two spindle nose threads - 1/2"-24 on the WW-II vintage 109.0703 and 1/2"-20 on all of the postwar ones. The latter is far more common.
The Jacobs 6B, 7B, 30B, 32B and 33B were all available with 1/2"-20 threaded mounting. CAUTION - each was also available in at least one other thread, so check that in addition to model number and condition. The various models have various chucking capacities from 0"-1/4" up to 5/64"-1/2". As nearly as I can tell from the Jacobs catalog, none have a through hole. However... In the catalog paragraph on removing tapered arbors from chucks, the text says that the chuck body is soft (that's relative soft, of course) and it is acceptable to drill a hole through the body in order to use a press to remove the arbor. So you can drill through the chuck the same diameter as the spindle through hole. Which should be 1/4". If your work pieces larger that 1/4" dia. only need another inch or so of length, on a 0-1/2" capacity chuck, you should be able to drill through up to about 7/16" dia.