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To answer your question, no, たらと does not represent two conditionals together. The と here is being used as a quoting particle, while the たら is the usual conditional. The verb that follows the と is the expression ため息をつく, which means "sigh" or "breathe a sigh". As such, what comes before the と marks what the speaker is sighing about.
I can understand why reading this is a bit confusing: the たら should typically lead onto another clause stating the result. But, perhaps exactly because he's sighing (which suggests this is an internal monologue that doesn't have to be fully formed), or because the logical conclusion of the thought is fairly obvious (that it would be good if the person the speaker is talking about could put the same enthusiasm into studying), the speaker doesn't finish the sentence. Ending a sentence on たら has the sense of "If only ...".
It might be easier to parse this clause if I add punctuation as follows:
Putting this all together, you might translate it as:
I often sigh "If only he could put this (sort of) enthusiasm into his studies...".
Hope that helps to clarify your understanding of the sentence.