For some people who like to follow a single stream, sure thats what they choose but in general the answer is no.
You can pick what you like and what is appropriate for you and your child.
I sent my kids to a local nursery (Lingnan) followed by a private-local Mandarin school (KCS) followed by an international secondary (KCIS)...
It gets much harder to switch later in age, it is also much harder to switch from international into local but for purposes of Nursery/Kindergarden, there are no real restrictions.
Some nurseries/kindergartens will give students priority when time comes to pick primary, but this is not a general rule. Only some will do this.