You can not check charging system output, VDC and VAC obviously if the bike is not in running order. But, you can check the Stator for any opens. Using an Ohm meter, place one plug of the meter into one side of the plug in Stator (in engine case) and place the other plug of your meter to the engine case itself (ground) do this with both wires in the Stator plug, one at a time. If you are showing resistance, you know the stator has an open and is shorting itself to ground and you will need a new Stator.
Yours being an older model, you should have a Maxi fuse update to protect the charging system, not a circuit breaker. And this only protects the charging system, nothing more.
If smoke came from under the seat and you have nothing with key switch on, most likely it is the EHC and Curtis will tell you that for sure :2thumbs:
As far as replacing it if it is bad, I would not go with the Wire Plus. They have been known to fail long before the factory EHC and they cost a hell of a lot more. Customer support is terrible if you have a problem. They have no problem taking your $$ to buy the POS, but when it fails in 15 months, they tell you your out of luck and need to buy another.
I would invest in a EHC that Curtis had or a Thunderheart Micro harness controller EHC.
Sounds like your batter needed to be replaced no matter what. Just make sure before you hook the new one up, you don't see any shorted wires under seat or anyplace else visible....and if you have a circuit breaker, change it out to a Maxi fuse.