No. A vacuum doesn't transmit heat at all. The chips will get very hot. Liquids (generally) transfer heat better that air. You can completely immerse your computer in 3M Fluorinert. That will transfer the heat. Then, cooling fins to transfer the heat into the environment.

The challenge is removing heat. Putting things in a vacuum chamber doesn't make them colder - vacuum is actually a pretty good insulator, so you'd need some mechanism to get the heat out of there with9out using air. If you go the other direction, some people have built computers they submerge in mineral oil or other similar media. That works pretty well for removing heat from components more effectively than air convection.

Yeah, but without air, the heat won't dissapate.

That approach would not be very different from surrounding it with sound insulation, and would involve the same challenges. Things that conduct heat out tend to conduct sound out too.

You'd still need to get heat out. You could water cool the machine, but you'd still have fans/radiator on the outside.

You could, but it would be thermally quite bad: The only way for parts to cool would be through radiation, which is way less effective than convection (be it forced by fans or passive, as in OP's design.)

You'd have problems with getting rid of the heat if your components were surrounded by vacuum - you'd only have radiation, no convection to carry away heat.