Technically, the Woody collective COULD exist in the Toy Story canon.
Hear me out
The first film and the TV special “Toy Story That Time Forgot” establish that, when a toy is based on some character from a show, etc., they tend to initially believe that they are that character.
We also know from the second film that mass-produced toys are initially indistinguishable in personality.
So, hypothetically, there was a canon point at which hundreds of Woody dolls were produced as merchandise for the Woody’s Roundup TV show in the 1950s, and each doll was convinced that he was Sheriff Woody,