Invisalign with Veneers for Overbite and Slight Overjet?

There should be no problem with Invisalign and veneers as the aligners simply put pressure on the teeth for movement. The alternative (bonded brackets) could damage the surface of the veneers, so Invisalign is likely the best option.
If the veneers pop off, there is something wrong with them. Bonded veneers are very strong and normally need to be cut off if changes are needed.

The only thing I would worry about is the possibility that the teeth with veneers on them will be shifted and the gums will no longer cover the veneer margin (the spot where the tooth and veneer meet). This may not be a problem if the margin is not detectable, but if the tooth under the veneer is dark and the veneer is light, you may have to replace the veneers for cosmetic reasons if the margin is visible. That said, it is unlikely the margin will become exposed, but you should consider the possibility.
If the veneers pop off that may mean the bonding wasn't very strong, and you should be able to rebond the veneer to the tooth without a problem.

You should be fine to use Invisalign if you already have veneers. If the veneers pope doff, it would be because there was something wrong with them that NEEDED to be fixed (blessing in disguise). And just FYI -- a healthy bite is one with a little overbite and overjet -- if your teeth were end to end (or edge to edge) there would be unhealthy forces on your teeth.