Will this dent be covered under Apple Care+ ?

Here is some Apple legal documentation for AppleCare+

Legal - AppleCare+ for Mac - Apple

Note this wording from that document:

Apple will not provide Hardware Service or ADH Service in the following circumstances:

(a) to protect against normal wear and tear, or to repair cosmetic damage not affecting the functionality of the Covered Equipment;

...

(e) to repair damage caused by reckless ... conduct, or any use of the Covered Equipment in a manner not normal or intended by Apple

I think the key is in (a) since this looks like cosmetic damage that does affect the functionality of the equipment. UNLESS ... you cannot fully close the laptop lid due to this damage, can you? (Because if the lid will not close properly now, I would then say it does affect functionality and would argue this should be covered.)

As for (e), I doubt that applies to you as this happened unintentionally by accident I am sure ... but an evaluation might conclude that such cosmetic damage was due to carelessness (dropped the laptop?).

Bottom line: I think because of (a) above, this is cosmetic damage that does not affect functionality of the device so I expect that Apple will not provide AppleCare+ coverage of cost to repair. Which, based on HWTech's post, will be a substantial cost.

Will this dent be covered? Based on the photo, this looks like a dent to the external aluminum enclosure/corner.

If you have an accidental-damage protection plan that specifically covers external enclosure damage, this would generally fall into that category. The important distinction is whether the dent is considered accidental damage rather than normal wear and tear or purely cosmetic damage.

Coverage can also depend on whether there is any additional damage affecting the device. In your case, if this dent resulted from an accidental impact and everything else is working normally, it looks like the type of damage that would typically be assessed as external-enclosure-only damage. Ultimately, the service provider would need to inspect it and determine the applicable repair category and fee.

If laptop functionality is not affected, then why worry about it?

It will not be free because that is either considered cosmetic damage (user pays for cosmetic issues) or it will be considered Accidental Damage.

FYI, since both the corner of the Display Assembly is affected as well as the corner of the Palmrest (part of the Top Case Assembly), this will incur two costs from AppleCare+ accidental damage incident. $99US for the Display Assembly (called "enclosure" in the AC+ documentation) + $299US for the Top Case Assembly (aka Palmrest area & keyboard....referred to as "Other" IIRC, basically everything except for the Display Assembly) for a total of $398US. This is not clearly stated in the AppleCare+ agreement, but this is how it works from my own personal experience. You will need to review this agreement since I cannot find the documentation on the Apple website at this time (Apple keeps changing things as well as types of extended coverage plans).

If everything is working fine and the laptop lid can open & close properly & fully, then why worry about some scuff marks & dents?