My short answer is: "no". That doesn't mean we shouldn't listen for God or the Holy Spirit's leading to answer our prayers, but never in contrast to God's revealed Word in scripture. Let's look at the use of that phrase, "be still", in this scripture passage and others throughout the Bible.
Psalm 46 is a short chapter, you should read the whole chapter to understand the context of that one phrase. It starts with verse 1 to set the overall context, "God is our refuge and strength, an ever-present help in trouble." It talks mostly of the nations in uproar, about wars, the mountains quake, etc... These are all physical things, and the message is that God is our fortress, we should be still (i.e. rest) in the comfort that God is all powerful and will be our help and fortress, we shouldn't worry or try to take things into our own hands.
This phrase, "be still" is found in six other passages throughout the Bible:
- Exodus 14:14, "The LORD will fight for you; you need only to be still."
- Nehemiah 8:11, "The Levites calmed all the people, saying, "Be still, for this is a sacred day. Do not grieve."" (they had been weeping and grieving as they hear the law read, they were told to enjoy food and drink, for the joy of the Lord is their strength)
- Psalm 37:7, "Be still before the LORD and wait patiently for him; do not fret when men succeed in their ways, when they carry out their wicked schemes." (again, don't worry, rest in God, everything is in His hands)
- Jeremiah 47:6, "'Ah, sword of the LORD,' you cry, 'how long till you rest? Return to your scabbard; cease and be still.'" (the first verse sets the context, "This is the word of the LORD that came to Jeremiah the prophet concerning the Philistines before Pharaoh attacked Gaza")
- Zecharaih 2:13, "Be still before the LORD, all mankind, because he has roused himself from his holy dwelling." (prophecy)
- Mark 4:39, "He got up, rebuked the wind and said to the waves, "Quiet! Be still!" Then the wind died down and it was completely calm."
If we use this passage in relation to prayer, or as an example of prayer we are practicing eisigesis (reading our own ideas into the text), rather than exegesis (shaping our ideas based on the text) of scripture. When we read our own ideas into scriptue, we can make it say anything we want, thus it becomes meaningless text and useless to us.
It should be as God tells us in Hebrews 4:12, "For the word of God is living and active. Sharper than any double-edged sword, it penetrates even to dividing soul and spirit, joints and marrow; it judges the thoughts and attitudes of the heart." If we read our own ideas into it, how can it judge the thoughts and attitudes of the heart?