Is it possible to use the BeMicro SDK as a pure FPGA device?

You could leave Nios II out of the design and use the JTAG to Avalon bridge and system console instead. So you could fill up some memory with your input data using system console, kick off your accelerator hardware, then read back the results over system console to compare the results with known 'golden' results. (You won't be able to use C2H this way though since you need a Nios II core present).