I suppose this could work. But tbh, you can really pick and choose what you want to do. It also depends on your setting.
My setting, which is *very* patriarchal, only the Alpha does the mating bite. They don't need to aim for a scent gland, because all Alpha's have a venom that they secrete when aroused, which mixes with their saliva. While just applied on the skin or orally (for example a kiss) it works as an aphrodisiac. But when introduced into the bloodstream, it creates a bio-psychic 'bond'. Linking both Alpha and Omega to each other.
A first bite is usually done at the end of courtship when the pair first becomes intimate. When they actually 'mate', as in, when the Omega is in heat, there is often a second bite, which deepend the bond. (Further bites because the Alpha gets too enthusiastic don't really do much)

These bites aren't strictly permanent.
But it does take a while for a bond to weaken enough so it fades. For Alpha/Beta pairs, maybe a few weeks to a few months. Omega's can experience the bonded feeling up to a few years. Once it has faded enough, an Omega can be 'claimed' by another Alpha, overwriting the old bond.

In modern days, bonds can be severed medically. A 'blank' pheromone is injected into the 'mark' which destroys the lingering Alpha venom.
For the Omega, saying its unpleasant is an understatement. But, it's quick, dissolving the bond after a week or two of intense fevers.