OpenEdge Progress Replication There's data sitting in OpenEdge Progress databases. We'd like to replicate that data to a PostgreSQL "datalake" using a software called HVR (high volume replication I think). What the software does is basically install a local agent and replicate data from a source DB to a target DB.

Does anybody know if Progress allows such a thing? 

I know it has its own replication mechanisms but that's not what we're looking for.
You don't have many options here:

1) if you are on OE11.7 and later, you can use OpenEdge Change Data Capture to track data and replicate it http://knowledgebase.progress.com/articles/Article/How-to-implement-CDC-Change-Data-Capture-with-OpenEdge

2) if you are on older version, you might use Pro2 software. I am aware of Pro2SQL for MS SQL target and Pro2Oracle for Oracle DBA.

https://www.progress.com/campaigns/openedge/Pro2v5-Webinar

EDIT: did not read the question in full: your best option is to ask Progress itself, but I don't see why not: your agent will be just another user connecting to database, so if you have enough user licences, you should be fine.

Edit#2: on older versions of OE Pro2 uses older solution to track changes: it installs triggers for tables you want to replicate, they fire up and record change in auxhillary database, then replication agent ran on Management Server actually replicate records to Target. Management server also contains tools to generate SQL schema updates, new triggers if Source schema changes, etc. 

CDC by itself allows you to track changed records but the rest is your responsibility: creating schema for target, generating SQL loads, etc. With newer version of OE, Pro2 utilizes CDC to speed up replication.