The short answer here is No.
And here's a little bit of why...
Your headshot is the link to your audience, your agent and your Casting Director. It is literally one of the most important things to have in your arsenal as an actor.
Of course, you might be the best actor on earth, however, if you can't get the call from the Casting Director to show this then that's not helping anyone, least of all you.
You may have an incredible portrait of yourself, but if it doesn't adhere to the 'rules' of headshot photography then you'll be seen as an amateur and the Casting Director will move (incredibly swiftly) on. The best scenario that you can hope for here is that they didn't even notice your headshot in the pile. It's easy to rectify this though! Get proffesional headshots and get remembered for the right reasons!
Ultimately the Casting Director is looking to employ you! They want to scan through the hundreds of faces on their desk/ in their inbox and find the right person. The right look, the right (proffesional) attitude. Then you can get the call, show them how good an actor you are and you're on your way to gainful and regular employment within your chosen proffesion!
I work closely with different casting agencies, I am grateful for this as it gives me an insight into the everchanging world of what is expected in a headshot. Different agencies within different genres and different countries all have their ideas of what is 'on trend' but there is a core of common rules that should be adhered to.
So while there are photographers out there that offer 'headshots', make sure that they are in fact headshots and not just great portraits.
A recent survey taken by members of the 'Casting Directors Guild' showed that 100% of the 175 members questioned said that headshots are not going away and remain one of the most important elements of being a proffesional actor.
So if you were thinking of getting your proffesional headshot portfolio, do your research. Does the photographer know the 'rules'. Do they know the industry that you work in and most importantly do you like their work?