Can an ethnic Armenian visit Azerbaijan?

No.

There were some cases when people with Armenian roots were not allowed into Azerbaijan even though technically they had 1/8th or even 1/16th of Armenian blood.

There were also some documented cases when Armenians just end up in jail visiting Azerbaijan. It's not the same as Armenian visiting Turkey.

If you can convince passport control that your last name is rather Persian or just sounds like Armenian by coincidence there's possibility you'd get in, but I would recommend nobody to lie.

The answer is not a strict no.

Officially and unambiguously, there's no such discrimination, as having such law would weaken the position of Azerbaijan in Nagorno-Karabakh conflict, where the proposed solution of the conflict by Azerbaijani side is the return of occupied territories to Azerbaijan while granting non-discriminating rights to all ethnic Armenians living within Nagorno-Karabakh.

But, there's a huge but. Namely, for example, about 20% of users having the same issue on this forum (Russian) said that they were refused to enter the country because of their surnames (-yan, -ian), which seems like the decision depends on the mood of the immigration officer. Also note that most of the users on this forum are Russian nationals who can visit Azerbaijan without visa for up to 90 days. In your case one needs a visa (unless he/she's arriving on a direct flight of Azerbaijan Airlines from New York City), so if one's already granted a visa there's a high probability that officers won't block the entry just because of the surname.

But before travelling or even applying for a visa, I would advise to contact US Embassy in Baku and get some assistance. Here you can see some safety during travel information about Azerbaijan from US Department of State Bureau of Consular Affairs. Unfortunately, it's also stated there, that:

Law enforcement officials have at times detained individuals from Armenia or with Armenian surnames for questioning or denied them entry into the country.

Also note that, as an Azerbaijani and originally from Karabakh I would welcome everyone to Azerbaijan without exceptions, but unfortunately not all people are open-minded, so keeping a low profile will help you to avoid unnecessary discussions.