Does patriarchal discourse underpin the construction of Banquo in Act 1, Scene 3 of Macbeth?
The discourse of patriarchy in Macbeth is not limited to Banquo. In fact, the entire play is structured around the lineage of kings - and this is passed on from fathers to sons, thus securing the continuation of male rule: the structure of patriarchy itself. But certainly, Banquo plays a role in this lineage.
Also, consider Lady Macbeth's famous line in Act One, Scene Five in which she calls on spirits to "unsex" her in order that she would become less feminine, more masculine, thereby more able to carry out Duncan's murder. This explicitly implies that a person must first be masculine to rule and secondly, one must be masculine to have the courage and power (no matter the moral means of achieving that end) to take over and rule. Lady Macbeth must be more masculine than feminine to have and exhibit power: the discourse of patriarchy shows itself here again.
But Banquo is important in establishing the continuation of patriarchy because his sons, according to the witches, will be kings themselves. Banquo is certainly not the tyrant that Macbeth becomes, so there's no way of knowing how oppressive his sons/descendants will be in terms of a ruling patriarchy. It is safe to say that the discourse of patriarchy constructs part of Banquo's role as acknowledging the continuation of patriarchal rule.
Thou shalt get kings, though
thou be none. I.iii.69-70.
It would be correct to say that patriarchal discourse plays a huge role in the lineage of kings as well as primogeniture in general in the context of the play's history and in Shakespeare's time. But to be clear, patriarchal discourse covers more than just the passage of power from male to male (this is Banquo's part in terms of patriarchy). Patriarchal discourse also refers to males occupying all or most positions of authority and the subjection of women to positions of less power and authority. This power imbalance between male/female doesn't really play a role in Banquo's construction but it is central to the turbulent relationship between Lady Macbeth and Macbeth.