And by the 2230's, would either Earth or Vulcan (or both) withdrawing result in the Federation dissolving?
Hmm. Hard to say. By the 2230s, the Federation is still young -- only about seventy years old. The loss of one of its key founding Members may well have led to the eventual demise of the Federation -- or maybe not.
I think it's clear that by the 24th Century, though, the secession of United Earth would not lead inevitably to the Federation's dissolution.
In fact, in the Myriad Universes
novel The Chimes at Midnight
, set in an alternate timeline where Spock died at the age of 8, the Klingon Empire ended up conquering Earth in a surprise attack in 2286, and the Federation government re-located to Vulcan. The Federation President and Council ended up using the Vulcan High Command Headquarters in the City of ShiKahr, seen in ENT's "The Forge"/"Awakening"/"Kir'Shara" trilogy, as their new seat of government.