We should indeed say that the Garch part of the model does not help to predict the Direction of the movement (this is given by the expected drift of the Arma, which gives the conditional mean of the return process) but helps to predict the size of the deviation of the next period return from the expected Arma drift. It is a measure of the squared size of the difference between next period return and its conditional expectation based on the Arma conditional mean. Which is why it is so popular in the risk management. The garch part answer the question: provided that the next period return will be different (to some extent) from my conditional mean prediction, how much will it be different? So it becomes very useful if you want to compute a Value at Risk on your strategy.
To this purpose, notice that it may be good to model a Garch even if you are not interested in the Garch per se, because it will contribute to removing the asymmetric and fat-tailed nature of the distribution of the shocks.. in other words, in an ideal world, you will have innovations that will resemble more closely a symmetric distribution with little excess kurtosis, which will help a lot in the risk management part of the strategy.
Not to mention that, of course, if you implement a good Arma-Garch model, and you are in the position to give a good forecast of both the drift and volatility, then you could switch to option trading (instead of equity trading like described) in order to boost your returns.. but this is another story..