No. For one thing, the Wardens are not royal generals of a standing army, their titles simplify military chains of command in national crises, but they don’t come with budgets and warehouses and staff officers. Most importantly for this particular crisis, they don’t come with fleets.
The problem that the Wardens of the North and West faced is that while they had land armies with which they could rush around trying to put out Dagon’s fires, they didn’t have the naval power to go after him directly. Nor did they have any authority over the only fleet on the west coast – the Redwyne fleet – that could have gone after him directly.
The Iron Throne did, but didn’t use it. And that’s a problem for the whole feudal social contract, because “a king who does not protect his people is no king at all.”