Yes, it can change you and therefore can change God's "decision" about what is good for you. Prayer is not a way of nagging God until He changes His mind about our fate. Rather, it is a means of changing ourselves. The order of the prayers serves to reinforce this idea even before we begin. The Talmudic Sages directed people to first engage in praise of God and only afterwards to request help from Him. When we begin by praising God, we remind ourselves of Whom exactly we are praying to and what prayer is meant to achieve. We then continue with our request, understanding that prayer is more than an eloquent kvetch.
Prayer instills a state of rest and tranquility, because as the individual prays, he increases his awareness that everything is in the hands of God. It is for this reason that our central prayer, the Amidah”
Internalizing this concept enables a person to feel less anxious, more secure and tranquil, no matter what challenges are encountered. Clearly, we should not be jellyfish flowing with the tides of life without exerting effort or trying to change direction. Nor is the positive aspect of every circumstance always obvious to us. On the other hand, we should realize that whatever may happen, we are in good hands.