In short yes! Of Course you can! If you're in the right place at the right time and a casting director wants you, then that could be you set for life! There are so many success stories out there such as Charlize Theron (fellow South Africa), who raged and roared at a bank teller in LA and a talent agent spotted her! And look where she is today!
Now I'm not saying you should go shouting at every bank teller in the hopes of being spotted by a talent agent, but strange things happen, if you're in the right place at the right time, that could be your break if you are just what they are looking for! (Hopefully that 'right place' is a casting)
But also ask yourself this, what are you doing?! Honestly, why don't you have experience when there are so many opportunities to learn? Get in contact with your local drama group or society and see if they or any near-by theaters hold any workshops? There are plenty of freelance trainers and casting directors who host workshops and some for a very reasonable price. It's not paid experience but it's definitely a start!
Also try find some small theatre courses or acting courses that might interest you and that are available at a decent fee. There are also plenty of student films in production that need actors who will work for free!! There are plenty of websites out there for you to make contact with these people and where they can advertise: such as here in Ireland we have the filmmakersnetwork.ie and crooked house theatre have a forum for advertisements. Also it might bode well for you guys out there with no experience to go and join things like Fishpond here in Ireland, run by a casting director and is viewed by many production companies that need irish actors (so why not see if there is an equivalent in your country?). Also Movieextras.ie is a great company, that charge about 60 euro for 6 months, and like 99 for the full year, and they will make your profile available to casting directors who need extras for filming in Ireland. The pay is rubbish but you learn all about what it is like to be on a film set and how everything works!
There are tonnes of ways for you to get experience, so go out and get some!! You can get paid acting work off the back of non-paid acting jobs!! Go and audition for the student films and learn the process of auditioning, get some work and make a showreel!
you can alternatively find some good scenes from films, tv shows or plays and film yourself and make a vimeo page, and upload all of those clips and send that link on to every casting director and director that you can get in contact with!! The work is out there, but if they don't know who you are they can't hire you can they?! (feel free to also write your own material! You never know, it could be your hidden talent and you could end up like Lena Dunham who wrote "Tiny Furniture", and "Girls"!)
So yes you can be an actor with no experience, and in my opinion it's not absolutely necessary to have training either, in schools and what not. It is a massive help of course, and you get to explore and learn so many different things, but it is not absolutely ESSENTIAL in landing you a job!!!
Best of luck! Get Experiencing!!