when I got my 57 panel long ago [it was maybe 35 yers old], it still had the original factory spare hangin under the back, never been on the ground - being in Canada it was the CDN version [Dominion Royal I think], and the place where I got new tires [Uniroyal dealer] gave me free radial tubes in all 4 if he could have that tire
old tires should be fine if they've not been exposed to UV, that spare was certainly "live" enuff to have been used, but I wouldn't count on them lasting as long as new, and I wouldn't pay much, if any, extra to get'em
Bill