@OK465: of course you are basicly right with the "be careful" . its not an approved procedure and there are situations ( departure e.g) where you should better not shortcut anything. thats why i mentioned doing this - when- enroute at cruise altitude, and only for smoothening the turn and of course not shortcutting several miles without a clearance . further you have to look at your next waypoint doing this "procedure" since it may happen the fms does not realize this shortcutted fix as passed and this may really mess things up ( thats why a "direct to" the next fix) . it may also be aircraft specific how smooth the system handles it when you do not touch anything.
In general we use it from departure to landing with the exception of radar headings
The LNAV just follows instructions from the source, be it VOR, ILS or FMS.
mutt, i do not think you will have much luck trying to fly an ILS with just lnav engaged on the autopilot - hoping that it will follow the instructions "from the source" .
hitting the app button may help a lot when established on an ILS or on interception course to final.