Is there a safe and compliant way to run consumer UPS power through house wiring to an outlet?
Yes.
You can run an isolated electrical line, using normal in-wall wiring methods, from a single inlet to outlets.
The inlet will need to be in the NEMA family.  A C13 inlet won't cut it for at least 2 reasons off the top of my head: first it lacks the necessary ampacity, and second it is voltage-agnostic, and the inlet needs to be keyed to reject a power source of the wrong voltage.
As far as having a built-in switch, same rules apply as for a generator.  You must have exactly one neutral-ground bond in the entire system.  Not zero, not two. (&quot;two&quot; is its own special kind of 'bad').  If the power source bonds neutral and ground, then you must switch neutral.  If it does not, then you must not.
The best bet is to switch neutral, but not bond neutral around the switch - have the isolated circuit draw neutral only from the switch.  These types of switches are expensive, so I'd just do cord-and-plug myself.
You would never have a reason to switch safety ground.