It may seem like a dumb question. Nevertheless I couldn't come with a logic.
It would take time so Vercingetorix and his men would be dead inside. However wouldn't they win the battle overall? Caesar would be in Vercingetorix's position.
You can find elements of answer in these earlier questions.
Basically, lengthy sieges weren't part of traditional Gaulish warfare, campaign fortifications appearing only late in the Gallic Wars, at the likely imitation of Roman tactics.
A lack of familiarity with it, the logistical nightmare that was implied in gathering tens of thousand people in the relief army alone without taling to build an even bigger wall (without any sort of help from topography) all the while doing so under Roman artillery fire or attacks, might have been important factors in sticking to a broad plan, likely decided during the last All-Gaul Assembly held at Bibracte.
Even if the prospect of Vercingetorix' death wouldn't have spelled the death of the coalition he led itself, which would have been almost certain, the lack of a clearly hierarchized command in the relief army "rear" headquarters ask the question of whoever would have decided it and how it could have been managed.
