My guess is that Linux will run just fine. The ARM architecture is generally well supported, as demonstrated by the Likes of Raspberry Pi, etc. Depending on the exact processor, not all features may be available from the beginning (Think efficiency cores on recent Intel CPUs), however Kyro was introduced in 2015, so its support has likely matured quite a bit already. (I note here that the 7c seems to be an SOC which includes extra devices like a Video interface of some sort. SOCs can be harder to work with, since they often have hardware installed that isn't commonly found elseware. I would suggest you search for guides for installing Linux on the exact model of notebook, or processor, and maybe searching for posts of people that have done the same to see if they have run into issues. Don't worry too moch though, the Raspberry PI also runs on an SOC, so succes is not unexpected)
The kyro architecture itself is a generation of Snapdragons ARM architectures, similar to Intels Haswell or Skylake architectures, both of which are x86 architectures and anything that supports x86 will run on them. So what you called the Architecture does not matter that much, especially if it isn't very new, and you should look at the instruction set instead.
That being said, you asked for a comparison wil an Intel i3. While I don't know about the c7's performance (or the i3 for that matter), I am going to assume that you plan to switch from the i3 to the c7. In this scenario you are switching from an x86 architecture to an ARM architecture. This means that not all software that you were running on Linux before will necessarily run on the new platform. Before you switch you should have look at the software you plan to run and make sure that it is available on ARM targets (or maybe even buildable, if you choose to build yourself). If you have a Raspberry PI or another ARM machine lying around, it may be worth trying to get you System and software running on there, so you would already have an idea of the challenges/problems that can Krise.
I hope that info can help a bit.