NotInitiated baskets should clear on their own, but Pending won't. Pending offline baskets can safely be deleted, but be careful with pending baskets linked to other gateways as they could be waiting for the payment to clear.
Is there any mechanism for cancelling or voiding the Payment Baskets?
No, not at this time, but we do have plans to review potentially adding a Void option.
What are the ramifications if I just delete these baskets?
For offline payments there is none. If they used a payment gateway though then that could pose a problem since it's waiting for information from the payment gateway to pay the basket.