Is it okay to run a switched and unswitched hot on the same neutral?
There is no problem with this. In fact it's very common, especially when wiring ceiling fans.  The power (2 wire /w ground) enters the switch box, then a switched hot and unswitched hot are supplied to the fan (3 wire /w ground).  This allows the light to be toggled by the wall switch, while the fan is toggled by the switch on the fixture. It's also a common practice to wire duplex receptacles this way, where one half of the device is always powered and the other half is controlled by a switch (in which case the tab separating the two halves should be removed on the ungrounded (hot) side). 

The grounded (neutral) conductor will carry the combined current of the two ungrounded (hot) conductors, so any inductive coupling will still be canceled out. Since the circuit is protected by an overcurrent device (circuit breaker/fuse), there is no way to overload the grounded (neutral) conductor. The current on the ungrounded (hot) conductors will be limited by the overcurrent device, so too much current should never flow on the neutral.