Verified answer

No, the shutter release and shutter speed are both fully electronically controlled on that model, so you do need a battery.

The original mercury batteries are long out of production as they were banned, but you can get a suitable replacement battery adapter from the link below.

According to Wikipedia, the battery is for metering and without it the shutter speed defaults to 1/500 second, so that implies that it will, but only briefly! See http://en.wikipedia.org/wiki/Yashica_Electro_35

It's no longer a primitive digital camera and batteries and movie are made for it. You do not must get an adapter for the battery,... simply move-reference the manufacturing unit advice. ..