If I have a BJT with a max Ic rating of 200mA and I drive in a base current which when multiplied with hfe, results in a theoretical Ic value of more than 200mA, will the collector actually draw in more than 200mA and get damaged, or will the collector keep drawing a max cap of 200mA? Is it safe to drive a transistor using base currents which would normally generate Ics higher than the data sheet cap recommendations?
A transistor doesn't have a current limiter - it will pass whatever current the surrounding circuit permits, if the base current x gain permits that current.
The Maximum Collector Current rating just means that the part is designed to carry that much current without damage.
When determining the maximum current a transistor can carry, you must also look a the collector/emmitter voltage drop to determine the power dissipated in the transistor.
You must design the surrounding circuit to ensure that none of the transistor's maximum ratings are exceeded.
It is not safe. The max Ic rating is an absolute maximum that the transistor can handle. If it draws more current than the maximum, it will overheat and break. Some ICs and microcontrollers have additional circuitry that sets and upper limit on the max current through the device or a specific pin. However, a BJT is a simple device. You have to design the circuit intelligently to avoid reaching the max collector current.