For those Baptists who teach their unsaved kids to pray in Christ's name, how does this make sense?

From the Larger Catechism:
Q. 180. What is it to pray in the name of Christ?
A. To pray in the name of Christ is, in obedience to his command, and in confidence on his promises, to ask mercy for his sake; not by bare mentioning of his name, but by drawing our encouragement to pray, and our boldness, strength, and hope of acceptance in prayer, from Christ and his mediation.

Can an unsaved heathen really expect to draw on the mediatorial work of Christ, something reserved only for the elect? Praying in Christ's name is reserved only for the saved.

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Scott Roberts
Ruling Elder, Lakeside Presbyterian Church (PCA)
Southlake, Texas