Will Invisalign Correct a Serious Overbite?

Yes. Overbites can be corrected using
Invisalign with aligner compliance by the patient and proper treatment planning
by an orthodontist.

In the UK an overbite means how much the top teeth overlap the bottom front teeth. Your question relates to how much the upper teeth stick out, hence overjet.

Invisalign can be used to correct serious overjets so long as the lower jaw/ chin point is not too far away from the upper teeth edges.

If it is not then Invisalign cane be used to tip back the upper teeth (so long as they are angled outwards).

If the teeth are not so tipped then I would recommend Invisalign with 2 upper premolar extractions.

This type of treatment takes upto 18 months as the top teeth have to travel a large distance.

We have done many overbite/overjet cases with Invisalign without headgear/metal braces or elastics.

Please, do not worry!!!! First set of aligners will not show any results - too early. Invisalign may not be strong enough for severe cases, but your Orthodontist can offer you a combination case - use a regular wire to help Invisalign a little.

In general Invisalign won't hurt you.  It will only work towards a better bite.  The question is how good will it get.  Invisalign is somewhat limited in its ability to correct overbites, especially in adults.  
If it is a horizontal overbite (properly called an overjet), along with significant spacing across your upper front teeth, you should see a significant improvement as long as you wear your aligners as instructed. But if it is due to a small lower jaw you may be disappointed in the results. Be careful taking advice from friends.  Your orthodontist is highly trained and since he said you are a good case, you likely are.

It sounds like what you describe (from an oral habit in the past, in this case thumbsucking) would be normally fine with Invisalign. The way an overbite is determined really is by looking at how the upper and lower molars meet. The molars can be normal and have what you describe.
Odds are, you will be fine and have a successful outcome.