Can I requst data too quickly from an I²C ADC?
Can I safely assume that the Linux I²C driver is taking care of this?


Yes, the TI Sitara kernel has full support for the so called I²C "clock stretching" that some chips use.

They don't allow infinite clock stretching and will report a bus error if the clock line stays low for longer than a defined period, but we're talking about seconds here, so no issue for your ADC.