No, you can be a part time trader or trade once a day or a week and still be successful. For me being successful in trading is having a profit so as long as you have profit in trading no matter if it is full time or part time. That's only my opinion about successful trader no matter how big or small you earn as long as you are having a profit then you are a successful trader.
I agree with you, the profit/losses we make will make us successful or unsuccessful traders! It's not everything about the time, not everyone can be a full-time trader and to make a profit with daily trading, I tried and that didn't work well for me! I am a lot better with mid and long run trades, simply buying when the market is down and waiting for better days is paying off for me! Of course, for mid and long run trades two things are needed, patience and strong hands!