Just so you understand. Your power adapter came with a one-year limited hardware warranty that only covers manufacturing defects. Regardless, an Apple Technician would need to examine the adapter to verify that it is.
You stated that you ran over it with a vacuum, which subsequently damaged it ... that's not a manufacturing defect. Just be prepared to get a replacement adapter at full cost to you. However, you may find the Apple Store employee sympathetic to your situation. You won't know until you pay a visit to the store.
You don't need AppleCare+, but in this situation, you may find that you can get the replacement adapter at a lower cost.