Last tested: Nov 16, 2017
Not exactly, but there are workarounds.
The problem is that Heroku only offers a streaming replica Postgres DB that is a read-only slave. This is because of Heroku's "hot swap" architecture, which basically means that the DB can swap out and become the production DB under certain circumstances, and therefore we cannot write to it.
You can use a forked database and use the Update Connection API endpoint to change the connection credentials programmatically, but that would be a unique approach. Here’s a doc for that:
However, the best option here is to setup an ETL pipeline to incrementally copy data from production Postgres to another database (Postgres, Redshift, BigQuery, etc...). This has the added benefit of creating a destination where you can load more than just your production app data (e.g. Facebook Ads, Event/Click Tracking Data, Email Campaign Data etc.) to create even more powerful end-to-end analyses.