Looks like it!
Just one thing though, this is almost certainly an Aylesbury mix and not pure bred, looks like perhaps white campbell or white layer, or more likely pekin crossed with Aylesbury. Pure bred Aylesbury ducks have very pale pink bills 99% of the time, if theres some yellow, its usually a mix of breeds. Older hens are also built a bit differently, with a sort of square shaped body.
That's all to say, you can expect more eggs to be layed and random gaps might be more odd.
With this very suspicious looking lady, caught yolk handed, I expect they are eating their eggs just as you thought. Though, again, it's very unusual for them to be able to crack their eggs- so I would before anything else, try to ensure good egg shell quality. Start offering crushed oyster shells if you aren't already, and you could also try calcium rich treats, such as calci worms