Hi Lisa,
Yes you are right, when you charge the phone when it is near dead, and the have a conversation, you need more power the the battery can supply, at least for more the several seconds/minutes, depending on how dead was the battery and how much power you need to transmit to the nearest cell station. If you are far, then more power is needed by the phone, hence emptying your battery even quicker...
Give the phone about 10 minutes before trying to establish a phone call...