Can we thus conclude, using the above verse, that polygyny is allowed and polyandry forbidden?
Yes. P. V. Kane cites this verse in the chapter on polygamy in History of Dharmaśāstra, Vol II Part I:
The Tai. S. (VI. 6.4.3) gives a dogmatic and somewhat picturesque explanation of polygamy that 'on one sacrificial post he passes round two girdles, so one man secures two wives; that he does not pass one girdle round two posts, so one wife does not obtain two husbands'. The Ait. Br. (12.11) similarly declares 'therefore one man has many wives, but one wife has not many husbands at the same time'.
Medhātithi, commenting on Manu 9.101, also uses the same verse in support of his argument that men are allowed to take more than one wife:
‘May mutual fidelity continue till death’,—this, in brief should be understood as the highest duty between husband and wife.—(9.101)
Medhātithi’s commentary (manubhāṣya):
‘Fidelity’—unstinted obedience in all actions. Says Āpastamba: (a) ‘The wife should not be neglected in matters relating to Duties, Wealth and Pleasure’;—(b) ‘The highest good of man consists in Duty, Wealth and Pleasure, as it is declared that the whole fabric rests upon these three factors.’
Some people hold the following view:—
“What is meant by ‘fidelity’ here is non-abandonment; otherwise, as to the woman, so to the man also, it would not be open to many more than one wife.”
This however is not right; because in regard to men there is a distinct sanction—(a) ‘Those who act through mere lust, etc.,’ (b) ‘the barren wife shall be superseded in the eighth year,’ and so forth; while there is no such sanction in the case of women. There is another text also which is indicative of the same fact—‘There are several wives for one man, but not several husbands for a woman at the same time.’
‘Until death,’—till they die; i.e., it ends only when either of them dies.
This should be understood to be the highest duty of man and wife, stated in brief.—(101)