how switch mode regs work - am I correct
It's the output capacitor that provides power to the load, while the inductor is made to squirt pulses of current onto the cap.  In a boost regulator (makes a higher voltage than the input power), the inductor only squirts current onto the output cap for part of each switching cycle.  During the other part, the inductor is being energized so that it can provide the next squirt.  In a buck regulator (makes a lower voltage than the input power), the switching is done on the input to the inductor.  It can always be supplying output current if that is how the supply is designed.

No, you should not change the inductance without understanding all the tradeoffs that went into deciding on that particular value.  There are various considerations, like the peak current relative to what the switch and the inductor itself can handle, ripple current on the output and input caps, total current delivery capability, and more.  Another parameter of inductors is their saturation current.  That you can safely make bigger, but not smaller without carefully understanding the design and being sure what the peak current thru the inductor is.