Allstates were never sold new in California, that is per Sears Roebuck & Company. The nearest Sears Auto Center licensed (by state governments) as a new car dealer was in Arizona. Either the original owner went there to get it or the sale in CA is an "urban legend".
Radiator hoses would be the same as on a Henry J, in fact virtually everything under the hood is HJ other than the branding of parts (Sears branded items were used for spark plugs, etc). The actual list of Allstate-specific parts is in a 1953 issue Kaiser-Frazer Service Bulletin. Of course, the accessories would be Sears-branded as well.
Anything with a single or double digit serial number in a K-F product is worth saving whenever possible. And remember, just because it's in the KFOCI Registry doesn't mean much...many of the listings cover parts cars, vehicles that have been crushed out of junkyards and other lost machines. Nobody bothered to indicate condition or plans for restoration for many, many years.