No, it's a subordinate (indirect) question. The direct question is 'In what order are the jobs done?', which corresponds to a statement 'The jobs are done in <some> order'. So 'in what order' is a preposition phrase (like 'in date order' in the statement), whether in a direct or indirect question.
The question form makes it harder to see structure, because elements are moved around. Look at the subordinate statement order first, then compare it to the subordinate question:
We know [jobs are done in date order].
We don't know [in what order jobs are done].
In both we have the preposition(al) phrase of . . . what would you call it, manner? I suppose so: a manner phrase, or perhaps an unusual kind of time phrase. It has the same function whether it's explaining the manner/time, 'in date order', or asking about it, 'in what order?'. It's inside a [subordinate clause], which can be either a statement or a question.
Usually it is the wh-word that introduces the subordinate clause:
I believe Mary.
I don't know [who to believe].
I left my keys in the bedroom.
I don't know [where I left my keys].
However, sometimes the front position is occupied by more than one word. Then we need to distinguish between the wh-word and the wh-phrase that contains it. The wh-word need not be the first word of the wh-phrase:
Your bicycle is red.
I don't know [what colour your bicycle is.]
The jobs are done in date order.
I don't know [in what order jobs are done.]
So, although 'in' is the first word of the subordinate clause (in the last example), it is not doing the job of introducing it: the whole three-word phrase is.
I would prefer to say that the phrase does the same job as an adverb ('sequentially', for example), but I would use a different name for this function. Often the word 'adverbial' is used for a function that can be performed by an adverb or another kind of phrase. In the Cambridge Grammar (CGEL), the term used is 'adjunct'.