The current will never get bigger than what the transistor can pass through. That's how they're used as amplifier in radios etc - a very low resistance load and the transistor regulates the current.
In your case you have a base current of 1.7 mA, and based on the data sheet the transistor will be able to supply >200 mA (collector saturation until about 100 mA), the data sheet that I found is not too detailed about this.