This is just how I would feel if this happened to me (wife):
If the woman my husband was cheating on was invited to my home without me realizing my husband was cheating with her, I would feel betrayed by both. I would feel like the idiot who didn't catch on.
If said woman hinted at being poly, I would be confused as to why she was saying this. Once I connected the dots, I'd be hurt that my husband did not come out to me.
If my husband had the audacity to bring the woman he is cheating with into my home, I would question my trust and his honesty. This would inflict a wound for me.
If this was how I was introduced to poly, I would be very hurt. It would feel like my husband is asking me to accept this woman or lose him. Worst of all, I'd feel like an idiot for not catching on.
I'm not trying to sound judgmental. And I'm not your wife - she may have different thoughts running in her head. If this were me, I would want him to admit to cheating first. I would not want the mention of poly to even be brought up. I would want some time to process this betrayal first. Once the initial emotional response faded and I was more rational - then I would be open to the poly discussion.
Again, this is just me.