Yes, Linux actually does already run on ARM chips, and Qualcomm themselves pledged support for Linux for the new chips within the next 6 months.
There is one big issue though: most applications won't be available since they have to work specifically for ARM. This is a big deal because I don't think Linux has a proper x86 --> ARM translation layer. That means most of your apps and games won't work.
I'd wait at least a couple of months to see how the ecosystem is before buying one. It's likely going to be a very bumpy ride for the next ~2 years until everything you'd need is supported.