There's no specific reason it shouldn't work. The main problem is going to be that your "granny' inner ring is going to be a couple millimeters closer in than the inner double and both rings are lower. On some frames and front derailleurs you won't be able to get the derailleur far enough in and down. But you may be able to space the crank out a few millimeters if necessary.
SRAM front derailleurs use the same cable pull as the older Shimano FDs and others, so if your SRAM FD won't adjust some other FD might.