I approached (hacked) this scenario once by having a child publication where we would publish the subset of PDFs to a separate folder, as configured in publication properties.
If I could revisit it, I'd first consider the business case as shaped by any technical restraints.
My use case was "authorized" documents that the business emailed direct links to. Luckily this profile didn't grow into more options, but if it did and we needed more folder variations a publication-approach would have be short-sighted.
No custom TBBs (same restriction in my case), seems to leave delivery-side code as the only way to handle the separation (maybe via a routing or redirect approach). But a better approach would have been pages.
So here are two more options:
Authors create pages with those to control placement of URLs in sub-structure groups. How they render is up to templating and delivery. This fits the scenario where the business emails links to these items. The event system or Page Types can help automate part of this.
Templates control SG placement through variants as determined in the linking component presentation. This gives you control over the path but might not be clear to authors without proper naming conventions or instructions. You would be calling "AddBinary" so I'm not sure if this would break your "no custom" rule.
Typically you would do one set location for variants per component template to avoid issues with paths.
The business or use case gives you more options than "yes" or "no."