Yes. A UNIQUE constraint is implemented with the help of a unique index - a b-tree index with default sort ordering over all involved columns. The index is created and maintained automatically, and is used for all purposes like a plain unique index by Postgres.
There is no need to create another (redundant) unique index like it, that would be a waste of resources.
Detailed explanation:
- How does PostgreSQL enforce the UNIQUE constraint / what type of index does it use?
- Is unique index better than unique constraint when an index with an operator class is required
Some rare exceptions apply for multicolumn indexes with special sort options: