Interesting question!
While Roderick Blackwood would certainly have a number of advantages that Arlan III lacked, I don’t think it would have been smooth sailing.
For one thing, despite the fact that his side has won, they’re pretty battered too and the Brackens aren’t going to go gently into that good night. So the new Blackwood dynasty would be starting out with a long bloody siege of its own vassals.
For another, the Blackwoods are in the religious minority, ruling over a kingdom that’s staunchly of the Faith of the Seven. And the Faith Militant is over the border in the Reach and unlikely to give up the ghost against a heathen usurper oppressing the faithful of the Riverlands.
And finally, the Blackwoods would have gotten themselves onto the throne with help from a foreign power. Arlan III is going to demand his price in blood and treasure just as in OTL, and that’s going to grate – how long before the Blackwoods are seen as quislings?