What about with the ST-E2? does this boost the range?
By boost the range, if you mean "can I use a smaller aperture?" or "will it mean less likelihood of underexposed pictures?", then one answer is "possibly".
The correct exposure is governed by a number of factors: firstly, the power of the flashgun, indicated by its guide number. The second factor is the distance the flash is from the subject. With a totally manual flashgun, you had to calculate the aperture by dividing the guide number by the flash to subject distance. For example, if the GN was 48 (m) and the distance was 6m, then the aperture would be f8.
Thirdly, the other factor that governs the 'range' of a flash is the environment its being used in. Using a flash indoors means that the flash light is bounced of ceilings and walls, effectively 'increasing' its range. Use the same flash outdoors, and the results will be very different as there's no reflected light to help.
Finally, when you're using a brolly, quite a lot of light is absorbed - this can be as much as 2 stops. You can mitigate this by bringing the light in closer - halve the distance between the flash and the subject and you'll recover the light lost by the brolly.
So, if using the ST-E2 means you can position the flash closer to the subject, then the answer is 'yes'. It won't make the flash more powerful though, as it's just a wireless transmitter.
It's a bit of a long-winded answer, but I hope it's useful.
Cheers
Mark