I think it's pretty clear from the coordinates that it is convex, no?
![Very Happy :D](./images/smilies/grin.gif)
Also, our current naming scheme is incomplete because it is ambiguous what the shape of the augment is. It is possible to augment a 3,4-duoprism with a cubical pyramid or a gyro square pyramid prism, and indeed, due to the shape of the 3,4-duoprism it can also attach to a tesseract, another 3,4-duoprism (in various orientations), etc., but the name does not unambiguously indicate which augmentation is meant.
But anyway, yes the Stott-expanded equivalent certainly should exist too. I have realized some years ago that for every augmentation of an m,n-duoprism with m-prism pyramids, there is a corresponding augmentation of a 2m,n-duoprism with m-gon||2m-prisms. I.e., a Stott expansion of the original augmented m,n-duoprism. I'm not clear exactly what the conditions are for augments other than m-prism pyramids, though.
In any case, even just within the confines of m-gon||2m-prism augmentations of 2m,n-duoprisms, there is still research to be done on counting exactly how many such augmentations (modulo 2m,n-duoprism symmetry) exist as CRFs. Marek & myself have already counted the n-prism pyramid / m-prism pyramid augmentations of m,n-duoprisms; there are 1633 such augmentations. I wrote a program for counting all augmentations with n-prism pyramids / n-gon||2n-prisms, and got somewhere around 1.6 million (most of which are caused by the combinatorial explosion of augmentations of the 20,20-duoprism, which are possible thanks to the very shallow height of 5gon||10-prism). However, this count was never independently verified.
If we include other augment shapes such as n-pyramid prisms, the counts will have to be adjusted accordingly. Though I doubt it will add significantly more augmentations to the total, because the 90° dichoral angles of the n-pyramid prisms would mean that only 3,n-duoprisms and 4,n-duoprisms are augmentable with them, so they would not experience the same kind of combinatorial explosion the augmented 10,10-duoprism and 20,20-duoprism exhibits.