You just so happened to ask me the question where I actually am CERTAIN about the answer.
I have been studying the lethality of broad heads vs deer for 42 years. And I can tell you with EXTREME confidence your answer is NO!
I have personal experience with EXACTLY 366 compound bow kills, 61 in just the past 3 years. And with every type of broadhead known to man.
And 20 different bows.
I have also been involved personally with a total of just over 1000 blood trails.
I can honestly and accurately say this...all deer are different. It is extremely difficult to categorize them into distinct groups when it comes to behavior, especially when it comes to different herds of deer in different counties, states, regions.
But in general, calm, lone deer, with floppy ears and relaxed tails, licking, scratching, and chewing, are your best target animals. But in order to keep this deer within a few yards of the arrow impact there are a few other variables that need to be present.
NEVER use a crossbow if keeping a deer close after the shot is desired. The noise from the shot is terrifying.
Never use a mechanical that opens with a "whacking" sound as the blades slam open.
Never take the shot in calm, quiet conditions as a background noise like wind, traffic, leaf blower, overhead airplane, helps dramatically to cover the sound of the release of the arrow.
An EXTREMELY sharp cut on contact head is best.
Remember, heart shot deer often run HARD AND FAST.
Bone shot deer run hard and fast.
Double lung shot deer through center lungs are your best bet.