Keep in mind that if he only has a position in one strike and is delta and premium neutral, then he has either a reversal or a conversion, in which case he locked in his profit or loss when it was executed.
What I think you mean is this. Imagine a local buys 110 calls at a lower IV and sells 111 calls at a higher IV, and manages his position until expiration such that it is at all times perfectly delta, vega, theta and gamma neutral (this is impossible of course, but just for the sake of argument). At expiration, yes, he will realize the theoretical value of the spread.
Specifically, let's say that at a volatility of 50%, the 110 calls are worth $3 apiece, and the 111 calls at that volatility are worth $2 apiece. So the spread at that moment has a theoretical value of $1. He buys a hundred spreads for $.90 each, a theoretical edge of $.10 x 100 = $10.00. If he can manage his position with perfect delta and premium neutrality until expiration then yes, at expiration he will realize a profit of $10.00.
As an early teacher of mine liked to say, "All options go back to the sheet (their theoretical value) at expiration."
