No, it's the other way round - a SRAM needs more cable pull per click (which is why it is more resistant to muck etc).
I think you'll struggle to pull enough cable for a full range of gears - but the best thing to do is try it out.
There are some little tricks like filling out the cable groove of the thumbie with strips of insulating tape to increase the radius.
I would probably try with a road lever on a Paul's thumbie mount as this has a bit more clearance all round to increase the diameter. SRAM also do road barcons (for TT bikes) and you can fit one of these onto the Paul's mount.