Depends entirely on the broker, and how the trader is trading. You'll read stories about it.
The smart broker would use that information to their own advantage rather than ban the trader. Or just be happy to collect their commissions.
No it depends on the broker as honest_knave pointed out above.
If you or your EA is winning bigtime and you have a broker that keeps the orders inside and plays the other half of your trades, then they will lose a lot of money.
And they do not want that.
There are so many different models used by brokers. 'A' book, 'B' book, hybrids etc. It really does depend on the broker.
But TBH, you probably don't want to use a broker that would ban a profitable trader anyway!