Can a view use a schema search_path?

My plan was to have two schemas: one for the live data, and one for staging, training, and testing.  Both schemas would have identically-named tables.  I wanted to create a single view in the public schema, and have that one view refer to the tables in one or the other schema depending on my search_path setting at the time I query the view.

But it seems that at the time the view is created it decides which schema's table it's referring to, even if I don't explicitly qualify the table names with the schema name.
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Adam Mackler