Of course it’s possible, it depends on the circumstances – I don’t think the Gardeners would be stupid enough to do it on their own, at a time when there was a strong monarch who commanded the support of the other six kingdoms, especially since even Mern IX was smart enough to ally with the Lannisters before confronting Aegon.
Rather, I think the Gardeners might well try to seize on instances in which the Iron Throne was weak and preferably already in the midst of a civil war to try to gain more autonomy within the system, or gain their independence if they think they could manage it.