Does a dual-SIM Android phone running only one SIM yield almost the same battery life as a single-SIM phone?
Will both the radios be running all the time regardless of whether both the SIMs are present?
Battery life (talk time and standby time) of active dual-SIM mobile phones is reduced, typically by about a third. For instance, Device manufacturer Samsung declares a standby time for its Champ Duos E2652 Dual SIM phone of 476 hours when used with one SIM card and of 322 hours when used with two SIM cards. To compensate the shorter battery life, some Dual SIM phones ship with better capacity batteries, for example newer Lenovo P780 have a 4000mAh capacity.
Wikipedia also describes different types of dual-sims, such as:
UPDATE 2013-09-23: The answer to your 1st question is NO, as described in the quoted Wikipedia text above. For your 2nd question, I don't know, but I assume it wouldn't run since there is no SIM. Probably also the reason why it consumes lesser battery.
If one SIM used on dual SIM phone, then the battery life increases. It also depends upon network range, i.e. if poor network connection then it consumes more battery than usual.