Will an 11-speed SRAM shifter work on an Alfine 11?
No. SRAM shifters (and regular Shimano shifters) don't have the right cable pull to deal with an Alfine hub. 

You need the Alfine shifters or ones marked to be compatible with Alfine (Jtek barends and Versa brifters are two of the 3rd party options for road bikes, for example).