Hier mal die aktuelle Ansicht eines SEHR erfahrenen US-Fluglehrers, der zu den maßgeblichen Figuren bei COPA gehört, zu dem Thema: "Direct zum FAF".

This is not allowed. It has nothing to do with the autopilot. Going "direct to" is forbidden by the complicated guidelines that the FAA and other "terps" exerts have established. You must be established on a leg to the FAF rather than going "direct to" because your "guidance" to the FAF must be on a path (magenta or green line) already lined up with the final approach course. There are some rare exceptions (due to terrain or airspace) where the course to the FAF does not line up the same as the final approach course. But even there, that leg to the FAF must be the path followed.

So, in summary, if you try to flt direct to the FAF or fly a path that does not intercept the course to the FAF, the approach will not be followed by either the autopilot or the navigator. The reason why you do not see this in any autopilot manual is because it is already implied by the "approach rules". You will see a hint to this in reading the navigator manual when it talks about how an approach path gets captured and its criteria.

If an ATC controller gives you direct to an FAF, that is only allowed (at least in the US) on a VFR flight where the FAF is merely being used as a VFR checkpoint. You cannot fly an IFR approach in that manner.