A lot of newer GG barrel chambers have very hard angles to their throats that can be close to 45 degrees! Those angles will strip a patch off if the owner shoots paper patch bullets. Most PP chambers have gentle angles of about 11 degrees or so to ensure the patched bullet enters the rifling before it begins to cut the paper.
Freebore is really designed for the weight and shape of the bullet to allow heavier bullets, or bullets with more rounded ogives to seat out properly and not have to be seated too far back in the case to chamber. All of my old single shots have gentle leads into the rifling, and enough freebore to handle seating bullets out further. But I've had new barrels installed occasionally and found I had to adjust seating depth to shoot them, or have the throat reamed to a gentler angle to allow a normal seating depth.

I think any competently-done grease groove bullet chamber should be able to handle paper patch bullets, after the parameters are worked out and complied with.  Most of the reproduction single-shot black powder cartridge rifles are chambered tightly, for target shooting, and both types of bullet can be used.

A classic "paper patch chamber" is basically a mechanical fit with the factory cartridge case.  The paper-patched bullet is of a diameter that is just large enough to be pushed through the barrel with a cleaning rod after two wraps of patching paper are applied.  The cartridge case never needs resizing; the patched bullet is simply inserted into the case mouth an eighth of an inch or so, with possibly a slight mouth reduction to keep it from falling out again.  Most of the bullet protrudes into the rifling.  When the black powder charge deflagrates, the bullet is slugged or riveted up to the bottom of the rifling grooves from the rapidly-expanding gases and the load of solid particulates generated from combustion.

A groove-diameter grease groove bullet when seated in a case will expand the chamber neck so the cartridge won't fit all the way into in a paper-patch (only) chamber.

Randy Wright's book is the best in-one-place exposition on the how-tos of paper-patch bullets, but the Shiloh Rifles forum and the Paper-Patch section on the Cast Boolits forum has a lot of good info as well.

When you say a mechanical fit do you mean the chamber with its gradual leade hugs the cartridge and seated bullet along its entire length?

By "mechanical fit" I meant that the cartridge case does not expand on firing and does not need resizing or neck sizing.  You deprime, reprime, fill with powder, seat bullet and load.

Eventually, after many firings, the shells might begin to stick, but by then, most had probably cracked or expanded primer pockets from much use.  By the time the modern solid head cases came along (as opposed to folded-head or "solid head" that were really semi-balloon head cases), paper-patch bullets had pretty much gone out of use.

Mr. Klinger is right--the Dual Diameter paper patch bullet is a modern innovation that allows the base to fit in the shell that has been expanded in the grease-groove chamber.  Many of the older paper-patch bullet designs were slightly tapered to fit in shells having thinner brass around the mouth while the forward end protruded into the barrel.

Sharps offered a "shell mouth reducer" to tighten the shell mouths around the bullet (if necessary) so it wouldn't fall out with handling.  Modern users of straight shank paper patch bullets get this same effect by running the cartridges into a proprietary neck sizing die, partway up a full-length sizing die (with the innards removed), into a special neck-bushing die or into a homemade die of some kind.  The seat-and-crimp die on a standard die set is not recommended for this job; it will cause the paper to tear when the cartridge is fired.