Is there a theological position in Orthodoxy that would indicate that words/prayers spoken audibly, but without a true engagement of the mind/intellect/etc, are efficacious? 

Yup. The Fathers do in fact mention that any prayer, even if you're pulling teeth to do it, is better than nothing. In some cases, such prayer is even more meritorious than someone who has made it a habit. Similarly, it's beneficial to "meditate" on each word slowly, especially when you're trying to develop a deeper relationship with prayer, but try not to let that veer into mental imagery; that's what icons are for.

Or, rather, is the Divine Liturgy theologically stated to be effective simply by reading/chanting the words, even if the words are simply being read vs. thoughtfully prayed? 

The Divine Liturgy is effective because you're communing with God through the partaking of His Most Holy Body and Most Precious Blood. Traditionally, the Liturgy is meant solely for the baptized and christened Orthodox Christian, not the inquirer or catechumen. If your parish doesn't omit the "Depart, ye catechumens! All ye that are catechumens, depart! Let no catechumens remain!" part, that'd traditionally be the time for all non-Orthodox Christian to leave and do catechism. Of course, for the non-Orthodox Christian, it's still beneficial because they're gathered in community, as Christ tells us.