Can I run a microcontroller on the power from a go-kart alternator?
This is really crying out for a switching power supply.  The input voltage can vary over a wide range, and is generally quite a bit higher than the 5V out you want.  You might be able to find a off the shelf unit that can handle your wide input voltage range.  A linear regulator would get quite hot.  At 50V DC in, 90% of the power will be dissipated as heat.  That's not so much a issue of wasting power, but rather dealing with the heat.  For example, if the micro and LEDs draws 100mA at 5V, then 100mA * 45V = 4.5 Watts will be dissipated in a linear regulator.  And that's with 50V DC in.  50V AC will produce more than that DC after a full wave bridge, and you say 50V AC isn't even the upper limit anyway.

In addition, something doesn't add up.  There must be DC somewhere used to make the spark.  Does the unit really not have a battery already?  That sounds unusual for a alternator system, although your voltages are in line with a alternator as apposed to a magneto.  How is the high voltage for the spark produced?