It should not, but it is depends upon the facts of your VAWA case that resulted in the I-360 approval. At times, a permanent residents file will be reviewed at a naturalization hearing. You may want to have an attorney assist with the naturalization process and be present at the naturalization examination and review.
If you have been a permanent resident for less than five years, then you will have to wait until nearer to the fifth anniversary of receiving your green card to file for naturalization, where you married a U.S. Citizen. If there is additional background in your record that can serve as grounds to deny or refer to immigration court, then you may want to carefully review the situation to makes sure that there are no unknown complications.
I strongly recommend an appointment or teleconference with a candid and experienced immigration attorney.
The above is general information and does not create an attorney client relationship.