Note that this is a question based on what is described in the book, rather than a question based on current actual quantum and/or cosmological physics. It wasn't quite clear to me from the discussions of wormhole transport: is it possible for a wormhole "end" aka entrance to be transported via an existing wormhole? There's a lot of description of the ships which carried wormhole ends at STL but I don't recall any mention of taking a "shortcut" via wormholes partway to the final destination.
There's no mention in the book of the ability to carry a wormhole entrance via an existing wormhole.
That said, if it was possible to do so then logically we should see that connected systems would have multiple wormholes strewn along the the path between them and the nearest system allowing for rapid re-emplacement in case a wormhole mouth is lost by accident or destroyed by enemy action.
We know that wormholes can be "emplaced" anywhere where there is sufficiently low gravity and that their destruction is "cataclysmic". We know that they can be used 'in transit' (e.g. without being emplaced at their final destination) since the Engineership Est-taun Zhiffir is able to be used as a router for discussion with the Omnocracy that should have taken a round-trip of over 300 years and we know that multiple portals with multiple destinations can be present within the same planetary system and probably also within the same lagrange point.
"Portals were only ever positioned at Lagrange points or other orbits distant from large heavenly bodies because they needed a section of space-time that was relatively flat. Too great a gradient - too near the gravity well of a planet or other large object - and they stopped working. Increase the S-T curve only a little more and they imploded and disappeared altogether, usually violently. The hurtling asteroid-ship was so massive and its velocity so close to light speed that it had the same apparent mass as a planet the size of Sepekte. The passing of its gravity well so close to the portal mouth, especially at that extreme velocity, was sufficient to collapse the portal and the 'hole beyond, sending one more cataclysmic pulse of light flashing throughout the system".
Since there's no mention of using one wormhole as a waypoint for other wormholes, we can reasonably assume that wormholes need to be carried the long way around (e.g. in real space) in order to function correctly.
I would assume that it is possible to transport a wormhole end via a wormhole, if the wormhole end has a "deactivated" state, in which there is no hyperspace connection present.
One would have to assume that the wormhole end is transported in that deactivated state, moved to an appropriate location (eg no gravity gradient), and then "switched on". While it's in its deactivated state it may be just another chunk of machinery with no special requirements, and thus can be carried through a wormhole.
However, there may be some kind of pre-connection (enough to maintain the connection between point A and B, but not big enough for something to travel through) through hyperspace which is maintained during the voyage. If this is the case, then it probably wouldn't be possible to send the portal through a wormhole.
The point @Richard makes about multiple wormholes between systems, to more easily recover from portal destruction, would make a lot of sense either way, as would a large degree of redundancy, eg five wormholes per system. The only possible reason i can think of why this wouldn't be the case (whether "portals-through-the-wormhole" is possible or not) would be that the wormhole creation and transport is so fabulously expensive that the Mercatoria can't afford to do it.