I probably didn't explain it clearly enough - the whole area where the
balusters are is boarded over, not individual balusters. There's two
big pieces of plywood covering the whole baluster area. What I'm
curious about is what's behind these two pieces of plywood - proper
balusters or just a few supporting struts holding up the handrail.

Sounds like a typical bit of 1970's modernism. I think the odds are in
your favour that the diy'er will have made the minimum of effort, and
lightly pinned the plywood (luxury! - it's usually hardboard) panels
in place.