MediaWiki database access abstraction layer supports PostgreSQL. Translate does not support PostgreSQL currently because the database table definitions have not been adapted to PostgreSQL.
If the table definitions are adapted to PostgreSQL, some testing is needed to confirm that Translate uses the access abstraction layer correctly.
Another question is whether it is possible to get continuous integration support for testing Translate with PostgreSQL to avoid regressions.
I think that when T191231: RFC: Abstract schemas and schema changes lands, we will get PostgreSQL support for almost no effort.