Looking at the video, it's kinda hard to say what it it, but that puff of smoke is less than encouraging.
Those carbs are not vacuum-regulated CV carbs, so absence of filters should not impact the running too much, if at all. However, if they are worn and have air and fuel leaks (internally, this won't show up as a puddle), that would be a problem. If they are just misadjusted, it's a weekend of screwing around. If not, it could be some months before you figure it out. Blue smoke usually means oil is burning, and the oil to burn can come from the valvetrain by way of worn valve seals and guides, or as blowby from worn rings and/or cylinders. Either one is a bunch of work.
I'm in my second year of trying to get a basket case XJ550 going...