The short answer to the title question is:
No. A person cannot contest a will that she has a fiduciary duty to uphold. See Love v. Cave, 622 S.W.2d 52, 57 (Tenn. Ct. App. 1981).
Likewise, an executor who “had knowledge of defects in the will but nevertheless proceeded to probate it,” is prohibited from challenging it.
So what can an executor do when a will may be invalid as a matter of law?
If (and this is a big if) she became executor without knowledge of the defect, and acted in good faith, she can resign as executor and file as an interested party. An interested party is one who would benefit if the will challenge is successful. The interested party need not challenge the whole will; challenging a single provision will suffice.
See the recent In Re Estate of Ellra Donald Bostic on this. While it wasn’t a page-turner factually, it does a good job going thru the law.
In Bostic, the trial court had ruled that although Bostic had standing to sue, she was prevented as a former executor. The Court of Appeals agreed that she had standing but said she was also not prevented from bringing the action unless she knew of the defect before she became executor. This was not shown or found by the trial court. Thus, the case goes back to county court.