Yes, Saginaw 3-speeds were used as the base transmission from '56 - '65 in the original "small case" design with non-synchronized 1st gear, and the completely redesigned "large case" design from '66 - '69 with synchronized 1st gear. The 4-speed became standard equipment in 1970.
A '66 Saginaw 3-speed should have the following casting numbers:
Maincase - 3858986
Tailhousing - 3873886
Sidecover - 3858992
Front Bearing Retainer - 3859033