My answer is No, mainly because most gamblers that deposit low or gamble at a low amount are strictly trying to avoid being addicted that's the more reason they are gambling with what they can afford to lose at a minimal percentage,basically because they don't want to get hooked up along the line so having used a minimum amount can't contribute to gambling addiction.
But what if they keep repeating that, they continuously adding money after every loss until they have no money left in their pocket? Or it's the last money they have. In that case, I think even a small (minimum) deposit could contribute to their gambling addiction.
The cause of gambling addiction is that we cannot control ourselves, so even though we play with small amounts of money but play many times, or play with amounts that we cannot lose. We can also become addicted to gambling.