I think it's pretty clear from the coordinates that it is convex, no?

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.