Will Intel Atom Processor laptops support cloned a Arduino with CH340 driver?
The processor in your laptop is irrelevant. It is the operating system you should be thinking about, not the processor.

If the operating system has drivers for the CH340 chip, and Windows does, as you already know since you are using it already, then you already know that the answer is a big fat yes.

The only time you need to worry about if the processor will support something is when you are switching to a completely different archetecture such as ARM.