I think this mainly depends on how isolated your environments are. Our dev and prod environments are isolated by firewalls, so the dev server cannot even "see" the prod server, so no, it would not work. However, if that is not the case in your environment, I see no reason it would not work. It would be the same as accessing a server datasource from desktop, which I do all the time.
Unfortunately this actually cannot be done. If you try to publish a workbook to one server that has a data connection to another Tableau Server, you will get a message like the following:
This workbook contains a Data Source that is dependent on a different Tableau Server. Multiple Tableau Server connections are not supported.
Error: Unable to connect to this Tableau Server data source.
You will need to create a local extract of the published data source. However this would no longer be "live" data. Let me know if you have any further questions.