I'm curious I've never seen a Android from China, especially with no Google firmware installed on it. What type of browser does that A5 and Note 3 come stocked with if any?
Samsungs usually come with their own S Browser, I assume what's it's called, their own apps are usually "S" something.

And the Coolpad will have it's own browser as well.
Coolpad is a Chinese maker and their website is only in Chinese, so I'm not sure how widely they're available elsewhere. May only officially be available in China. There are other Android devices that don't have Google and are not Chinese, e.g. Amazon's devices, they have their own Amazon stuff on them instead.
Also what happens with those devices when you login to your Google account from the devices if you tried?
Well you can't, that's it. In fact in China you can't really use anything Google unless you got a VPN, because it's blocked otherwise.
Google maintains a small presence at google.cn which is basically Maps and Translate, and not much else. Can't even do Gmail without a VPN.
That's all you get from Google in China...
Search directs to Google Hong Kong, but doesn't work in the mainland without a VPN.
Companies such as Baidu, Tencent and Alibaba have basically taken Google's place for Android, with things like app stores, IM, social networks, music, movies, etc. etc.
If I can get answers to these questions, there maybe other routes to take on obtaining Google Play Store and other important services from Google.
The only ways really for the OP's China devices, are what I've already stated, either find an appropriate international ROM, which may not exist for the Chinese Coolpad, or root and custom recovery, again the Coolpad will be a problem. Samsung A5, there's probably something on XDA Devs or SamMobile for it.