I'm sure that at first you will be addicted to that method, because it is really addictive because we will experience consecutive wins and I also think that the casino really wants us to feel that way so that we will keep playing gambling using the martingale method.
But when the casino sees that you are losing a lot at the casino, you will definitely fall into the trap of addiction, and when that happens, we should really take care of ourselves.
Martingale by itself does not have anything to do directly with gambling addiction, if we are objective and neutral on the topic, but it has much to do with the rapid loss of bankroll and recklessness while gambling, which could eventually indeed lead to addiction to gambling.
There can be someone who is responsible with their gambling and assigns a small amount of their gambling budget to try martingale for the sake of fun, they end up losing their money and would not chase it, because in the end they got what they wanted, to have fun with a little bit of money they could afford to lose.
I have never used martingale, because it is often associated to people who seeks to get profitable sessions and money out of casinos, which is very risky and does not go with my gambling style.