No. Novas will be tied to the platform they were purchased in, i.e. Switch, Xbox, Steam…
If the user has enabled cross-progression and plays across more than one platform, they’d have individual inventories of Novas for each platform, meaning they could have 500 Novas on Switch, 1000 on Xbox, etc., even if they can enjoy the items purchased with Novas on all platforms linked.
On top of this, there is a shared inventory that is multi-platform. It’s mainly used for the Novas that are obtained through the free track of the Tamer Pass and the free Weekly Challenges of the Tamer Pass. Those Novas will go to this inventory and they’ll be usable on any platform. The game will always use the platform-linked Novas first, as they are more restrictive.