Yes, you can do just the fuses - that's what I did to the 328 that came with my tester after I swapped the 8MHz crystal for a 16MHz. It wouldn't boot, I set JUST the fuses, then it would boot but naturally all cap values were off by x2 as was the output of the function gen feature.
Rather than make 2 posts - I just installed the K firmware for my AY-AT model using the 16MHz files. I have 2 brand new 328s, first one took the Flash and EEPROM no problem, but it just would not accept the efuse setting of 0xFC. So I tried the second one - same deal. Flash writes and verifies, EEPROM writes and verifies, but it will not accept efuse 0xFC. The one that came with my tester had no problem setting efuse. A little investigation says some 328's seem picky about setting bits that aren't actually used (maybe fakes? Maybe mine are fake?). The ACTUAL fuse setting when you use 0xFC is 0x04, so I set it to 0x04, it took that. First one, I got the whole screen to light up when pressing the encoder but it wouldn't start. The second one - success. Booted up, warned that it was not calibrated, etc. Ran through the cal (the original one wanted a 1000nF, this one asks for a 100nF). Kept showing the 100nF as 59nF. But resistors were right on, and other caps like a 220uF were within tolerance. I checked more ot the 100nF's in the bag - all came up 58 or 59nF. Double You Tee Eff? I don't have any others besides an assortment of ceramics and an assortment of electrolytics - testing a few others and they were fairly close, probably within tolerance. Then I remember, the BM235 DOES have a cap tester. So I tested one of these supposed 104's - it read 59nF. So what I really have are some dodgy as capacitors. Guess that'll learn me to buy cheap Chinese assortment sets. I tried a few at random and they generally match the marked value within tolerance, just this 104's are ALL way low.
Checked the function gen - up to the 400 and change KHz setting it's dead on per my scope, and only slightly off on the higher ones. 50, 60, and 100 are 50.00, 60.00, and 100.00. So it is the right firmware for a 16MHz crystal. Guess I need to get myself some fairly precision caps of the right values to truly calibrate it. Resistors are dead on, it detected the proper Vf for an LED I tossed on, and had no problem with an NPN BJT or an IRF540 N channel MOSFET. Looks like I have a winner. And it probably was ok with an 8MHz clock with the original firmware as well, it's those joke caps that were leading me astray.