No, for two reasons:
For anyone who speaks in a tongue does not speak to men but to God. Indeed, no one understands him; he utters mysteries with his spirit. 1 Corinthians 14:2 (NIV)1) Although this text says straightforwardly that a tongue speaker speaks mysteries to God, in saying so, is its intent to highlight the direction of tongues? No, in context, this passage states very clearly why a tongue speaker, in effect, speaks to God: because only God can understand him, no one else does. To people it's babble, to God it's understandable-- even if it was directed to men, only God would understand the language and comprehend the message. To extrapolate from that functional reality to say that tongues must be directed conversationally to God is to say more than, and other than the scripture says in context. Although there are passages which anecdotally imply direction toward God (in those instances, anyhow), that is not the same as asserting that the direction has to be toward God just because it was in those instances.
In the Law it is written: "Through men of strange tongues and through the lips of foreigners I will speak to this people, but even then they will not listen to me," says the Lord. Tongues, then, are a sign, not for believers but for unbelievers; prophecy, however, is for believers, not for unbelievers. 1 Corinthians 14:21-22 (NIV)
2) When Paul quotes Isaiah to point to an OT presage of tongues, he clearly reverses the direction of communication, i.e. God speaks to men through the strange tongues other men are speaking. If the model for tongues was directed from God to men, why would anyone doubt the fulfillment could be?
Since God inspires both the tongues and the intepretation, it is up to him to determine what is done with them, especially directionally. The only objective tests we are given in scripture regarding any spoken utterance deal with content, not direction. If we listened to the proponents of directional theory, we would wind up paying undue attention to the pronouns in a message rather than its actual content. What excess or error could that possibly address? Aren't there enough real problems for charismatics to deal with that we don't have to go around turning stones over looking for intellectual trifles to stumble over? Oy vey, from my tongue to God's ear!