Well, some of it is, I suppose.
As you may recall, ὦ ἄνδρες Ἀθηναῖοι, I expressed vexation at the long-standing claim that Classical Greek was allegedly a bit quodlibet when it came to word (i.e., constituent) order. Out of curiosity, I decided to have a closer look at a short section of Lysias’ On the murder of Eratosthenes and found that a high degree of regularity was the order of the day. Here’s the section in question.
 ἐπ’ ἐκφορὰν γὰρ αὐτῇ ἀκολουθήσασα ἡ ἐμὴ γυνὴ ὑπὸ τούτου τοῦ ἀνθρώπου ὀφθεῖσα χρόνῳ διαφθείρεται· ἐπιτηρῶν γὰρ τὴν θεράπαιναν τὴν εἰς τὴν ἀγορὰν βαδίζουσαν καὶ λόγους προσφέρων ἀπώλεσεν αὐτήν.
The subject of the first sentence is ἡ ἐμὴ γυνὴ “my wife”, which is modified by two non-finite verb clauses, αὐτῇ ἀκολουθήσασα “while she followed her” and ὑπὸ τούτου τοῦ ἀνθρώπου ὀφθεῖσα “seen by this person”. Note the structure of both of these. The complement (αὐτῇ, ὑπὸ τούτου τοῦ ἀνθρώπου) precedes the head (ἀκολουθήσασα, ὀφθεῖσα). Note also how αὐτῇ ἀκολουθήσασα, which is a modifier, precedes its head, ἡ ἐμὴ γυνὴ, but in order to avoid the whole phrase being top-heavy, Lysias places the second modifier after the subject and gets a nice modifier – head – modifier pattern.
I got tripped up by χρόνῳ “in time”, which actually follows the same pattern because it goes with the verb διαφθείρεται “she was seduced”. However, as a speaker of a VO language, my inclination was to take it with the preceding verb. Nonetheless, the sentence ends up being subject – adverbial adjunct – verb.
The second sentence shows a similar sort of patterning in some of its parts. τὴν θεράπαιναν τὴν εἰς τὴν ἀγορὰν βαδίζουσαν “the maid who was walking in the market place” follows the spec + noun + spec + modifier pattern (e.g. ἡ γυνὴ ἡ σοφή “the wise woman”), but inside the modifying phrase, εἰς τὴν ἀγορὰν βαδίζουσαν follows the adjunct/complement + head order. So does λόγους προσφέρων “addressing arguments” with the dO preceding the verb. αὐτήν “her”, on the other hand, stands in a marked position, which makes it emphatic.
The point is that Classical Greek had some sort of constituent order, albeit one that could, for whatever reason, be violated. However, this modifier-head pattern in the language could be helpful in deciding what to do with adverbial adjuncts: as a general principle, they might be taken with what follows rather than with what precedes.