Currently, we are having discussions on splitting the references sections from the main content in order to reduce the time to first paint for clients.

This makes sense if we are constructing pages on clients and not streaming page content. This is the current case. It is easy to demonstrate that removing references significantly reduces the size of the payload and reduces the amount of time to first paint in this scenario. See: https://www.mediawiki.org/wiki/Reading/Web/Projects/Performance/Lazy_loading_references

However, if we stream page content and the browser renders that content progressively, does it matter?

Basically, if we package and deliver our content in the way that browsers can handle most efficiently (streaming), then does the point about splitting out references become moot?