I'll try to explain with an example,
Assume Cluster CL-A has indices IND-1, IND-2, IND-3 and index IND-2 has documents DOC-1, DOC-2, DOC-3.
You took a snapshot SNP of index IND-2. After taking the snapshot, you add another document DOC-4 to index IND-2.
Now, if you were to try and restore the snapshot SNP in cluster CL-A then (as per my knowledge) Elasticsearch will thrown an error saying index with name IND-2 already exists and won't restore the snapshot. Alternatively, If you were to restore with a different name (IND-4) then your cluster will have indices IND-1, IND-2, IND-3, IND-4 wherein IND-4 will have documents DOC-1, DOC-2, DOC-3 and index IND-2 will have documents DOC-1, DOC-2, DOC-3, DOC-4.
In short, a restore of snapshot will not affect any existing index or documents within those indices.