No, that does not explain the subjunctive, because no reason or explanatory fact is introduced by the quod.
An explanatory clause looks like this:
Profectus est, quod constitutum cum aliquo habuit.
He set off because he had an appointment with somebody.
He had an appointment—you have it on my authority.
Profectus est, quod constitutum cum aliquo habuerit.
He set off because (or so he said) he had an appointment with somebody.
He said he had an appointment, maybe he did, but I haven't checked.
It may be called a form of indirect speech, although I would not classify it as such, because there is no verbum dicendi in sight.