To get the probability of hitting a target price you need a little more math and an assumption about the expected return of your stock. First let's examine the parts of this expression.
IV is the implied volatility of the option. That means it's the volatility of the underlying that is associated with the observed option price. As a practical matter, volatility is the standard deviation of returns, expressed in annualized terms. So if the monthly standard deviation is Y, then Y*SQRT(12) is the volatility.
From the above you can see that IV*SQRT(DaysToExpire/356) de-annualizes the volatility to get back to a standard deviation. So you get an estimate of the expected standard deviation of the return between now and expiration.
If you multiply this by the stock price, then you get what you have called X, which is the standard deviation of the dollars gained or lost between now and expiration. Denote the price change by A (so that the standard deviation of A is X).
Note that we seek the expression for the probability of hitting a target level, Q, so mathematically we want
1 - Pr( A < Q - StockPrice)
We do 1 minus the probability of being below this threshold because cumulative distribution functions always find the probability of being BELOW a threshold, not above.
If you are using excel and assuming a mean of zero for returns, the probability of hitting or exceeding Q at expiration, then, is
1 - NORM.DIST(Q, StockPrice, X, TRUE)
That's your answer for the probability of exceeding Q.
Accuracy is in the eye of the beholder. You'd have to specify a criterion by which to judge it to know the answer. I'm sure more sophisticated methods exist that are more unbiased and have less error, but I think it's a fine first approximation.