No. Variant calls are based on a reference genome sequence. Technically you could assemble the raw reads into a draft reference and variant call from that, but you'll still have to obtain some reference before you can perform variant calling.
EDIT: I may be incorrect in the case that you're working with well-characterized bacterial species and are looking for specific features. Check out this paper describing the KVarQ program. I imagine the same would be true if you're working with something like mitochondrial data.