Can I estimate Wi-Fi's power transmission in function of the amount of data transmitted?
If two radio systems are operating at broadly the same frequency, using the same type of antennas and over the same distance and terrain, a theoretical comparative judgement can be made. The judgement is based on the assumption that a receiver (at a lower data rate) requires less received power at its antenna compared to the receiver operating at the higher data rate.

The required power for a receiver is -154dBm + 10log\$_{10}\$ (bit rate)

Ignoring the -154dBm (because we are making comparisons) it can be seen that: -

10log\$_{10}\$ (200,000) = 53 dBm and

10log\$_{10}\$ (2,000) = 33 dBm

I've ignored "B" (bytes) and assumed "b" (bits) in the equation but it makes no difference; 2 kbps requires a power level at the antenna that is 20 dB smaller than 200 kbps for the same bit error rate.

In real money, that means one-hundredth of the power is required to be transmitted for 2kbps, all other things being equal.