Can a sentence be described as compound (rather than complex) purely based on the placement of the conjunction?

For example:

"Though he was late for class, he walked slowly down the corridor."
This is considered a complex sentence as "Though he was late for class" is a dependent clause.

However, I can change the placement of "though" without altering the meaning or any other parts of the sentence as such:

"He walked slowly down the corridor though he was late for class."
Here, there are two independent clauses ("He walked slowly down the corridor" and "he was late for class") joined by a conjunction.

Is the second version now a compound sentence, rather than a complex one?