... the crop receives only 1/2.56 of the amount of light falling on the sensor and so the noise is greater.
Your statement is partially incorrect. The flux is lower but the irradiance is the same or higher due to being concentrated on the smaller sensor. Hence exposure is equivalent. Any additional noise artifacts are due to sensor design, not exposure.
Anyway we're talking about superteles, where people are putting the same x00mm f4 on a crop or FF so this discussion is irrelevant. The flux and irradiance is identical for both sensor sizes.