Can a 17 year old have sex with an adult if the age of consent is 17?

Yes, they can.  Anyone over 17.

Not if the adult is in a position of authority over the 17 year old.

Age of consent means that the person can consent to have sex with other people of the age of consent.  An adult can still get in trouble with the law if the law wants to be nasty about it they can say that you sexually exploited a minor.  Even if the minor consented and gave their consent they're still considered a minor and there's still that sexual exploitation of a minor law which is a sex crime which will give you 15 years in prison if you happen to bump into a police officer that wants to be nasty and see that you get some jail time for it.

Yes,

The age of consent means that an individual that has achieved that age can consent with ANYONE of that age and older. Usually they can also consent with a younger individual due to "Romeo and Juliet" laws. 

In New York, there is a partial Romeo and Juliet exemption for consensual sex between a minor who is 15 or 16 and someone who is younger than 21. There is also a partial exception for consensual sex between a minor who is 11, 12, 13, or 14 years old, and a defendant who is younger than 17. This is a partial exception because, while these parties are protected from felony prosecution, they may nonetheless be charged for sexual misconduct (a misdemeanor), which can incur a sentence of up to one year in jail. Sexual contact with a person younger than 11, however, is always a felony, and a conviction can result in up to 25 years in prison, depending on the facts of the case.

https://www.criminaldefenselawyer.com/resources/ne...

I didn't realize the concept of "age of consent" was so difficult to understand.

Yes:  nothing illegal (OR immoral).