Yes but you will get less than if you had a charger. They will take just about anything. But older stuff you can only get credit, and if it's not a valuable game/system you won't get a lot. Newer/bigger name systems and games will get you more because they are worth more. Anything you are missing will detract from the overall value, that includes cases for games, chargers, controllers, etc. And the worse the condition that will also detract from the value because they will have to spend more time/money cleaning and repairing it.
Yes
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