On page 254 of the datasheet, you can see it takes about 14 ADC clock cycles to do one conversion. All you have to do is find the analogRead section of the Arduino code for the 8MHz chips, and figure out what register settings they're using for ADC and calculate the ADC clock. There might also be a lot of other Arduino fluff surrounding the analogRead function, kind of like the digitalWrite function...Arduino expands what should be 1 or 2 cycles into over 70 cycles.
So...you might just want to write some code to test it.
Or maybe you could rephrase your question to get the actual answer you need? "Can the Arduino sample the ADCs in full 10bit resolution at 250KHz?" would be a definite no, for example. 1KHz, definitely yes.