Can wisdom teeth coming through cause a really foul smell and taste in your mouth?

Yes. Impacted wisdom teeth that are partially visible in the mouth are a prime area for food and bacteria to harbor and can be a definite cause for a foul taste and smell.
Yes. If bacteria and food particles are accumulating around that area then the bacterial by-products of their metabolism will contribute to the poor odor and taste.
YES. When wisdom teeth are impacted and 'just breaking through the gums' they can get infected and cause halitosis (bad mouth odor). It actually happened to me. My oral surgeon removed all four of mine @ 45 years old with resolution of symtoms.

Related Questions

Wisdom teeth extraction site has a skunky taste and smell and a throbbing pain?

Possibly Dry Socket. If it was a few days ago when removed dry socket can occur esp. in lower teeth. It can easily be treated with pain relief by your surgeon : ) Have it looked at to also rule out post op infection. Read more...
Skunky taste. Combined with malodor and pain probably signals infection. May need antibiotics and/or medicated dressing as well as analgesics. Contact the Dentist or Oral Surgeon who removed the tooth for evaluation and treatment. Read more...
Dry Socket. Dry socket. Easy to treat. See oral surgeon For best results with wisdom teeth, make sure you are evaluated and treated by a board certified oral & maxillofacial surgeon. Read more...