I was asked that very question by a client this morning. The lawyerly, and probably not completely satisfying, answer is “not necessarily.”
When you fill out your FAA Medical Application, not only are you required to disclose drug and alcohol related arrests and convictions in response to Question 18(v), but you are also required to disclose any other misdemeanor or felony convictions in response to Question 18(w). In and of themselves, Question 18(w) convictions will probably not disqualify you from being issued a medical certificate.
However, keep in mind that the FAA is asking for that information to determine whether you are qualified to hold a medical certificate. Besides substance abuse/dependence, a disqualifying condition that the FAA tries to identify by asking for drug/alcohol related convictions, the FAA is also trying to identify other disqualifying conditions including mental conditions such as personality disorder, psychosis, and bipolar disorder. If the convictions are indicative of a disqualifying mental condition, whether substance abuse/dependence or some other mental condition, then you could be precluded from being issued a medical certificate.
Thus, a felony conviction by itself isn’t disqualifying. But, if the conviction convinces the FAA that you have a disqualifying mental condition, it will be that mental condition which disqualifies you, not the fact that you have a conviction.