Depends on the topology of the charging circuit if it would work or not, but most likely not, at least not if you replace the ALT light with a LED unit just like that. I would just let that ALT light be a regular bulb or mount a LED unit with a resistor parallel over it to simulate the charge/resistance of a regular bulb. It doesn't need to be a lamp to make the charging circuit work, so a resistor behind the dash cluster or tucked away near the alternator or regulator, will do the job just the same. Indication from the LED and the charging circuit stimulated by the resistor. A value between 5 to 7 Ohms should do it, a 4 or 5 Watt piece is more than enough. Standard resistor values are for instance 5.6 and 6.8 Ohms.
 

Hey Dave,
 
What type of LED's are you using, sounds like a neat mod, might do it myself while the instrument cluster is out?

I was having a quick look on ebay and found these guys:
 
http://stores.ebay.com/autokenz
 
Thought some of their dash lights might fit into the AMC bulb holders.
 
They also have tail light and indicator replacement bulbs.