Is it possible to install Deepin Store in Ubuntu Mate? Any chance it will be included in a future version of Welcome?
No, it is not recommended.
I don’t know if this works but you could try to follow this link 
http://www.noobslab.com/2014/05/deepin-software-center-v32v3021.html?m=1
Another suggestion will be appgrid.
Which is for Ubuntu and is lightweight, like Mate.
Way ahead of you 
Appgrid is already in new versions of Welcome.
Only using the console to install and remove applications does have its demerits, and you just caught one! 
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