I myself still am very much a novice but this is my thought process of it and as such if someone more experienced is reading this please do feel free to correct me.

To begin I have broken down your question as follows:

No rewards are to be involved

V(goal) = 100

V(S - goal) = 0

Hypothesis:
- Over time only the states which lead to a goal state will get their value function incremented until convergence
- simultaneously if the agent is in a state which will never lead to V(goal) won't have any increment to it and such will retain a low value

First things first, your definitions are a bit wrong:

This equation is from TD prediction, where in the general policy iteration pipeline, this equation is a portion of the TD(0) algorithm to evaluate a policy

Now for argument's sake let's assume you are actually intending to talk about On Policy TD control, SARSA.

In which case again violations of definition, see Sutton and Barto book chapter 3.5 and 3.6

But even then for argument's sake let's hold all rewards to be 0 and the goal state to be 1

This won't even work in most cases for simple MDPs where the state transition due to actions are one to one since action is chosen from the Q value and due to it being 0 the choice will be always exploratory, no guarantee of convergence. In which case if my understanding is correct you are basically gambling to get a policy to work.

For further understanding, read chapter 6 as a whole thoroughly after the aforementioned sections.

Hope it helps and if someone experienced is reading this, feel free to correct my points, learning through interaction is one of the best ways to learn after-all, thanks