yes, but with limitations, being a quad core (and the new battlefield optimised for 6 core) the cpu would struggle without streaming, because if you stream then the cpu would dedicate one (or possibly 2) of it's cores to the streaming (lowering frame rate) I would suggest a ryzen 5 2200 cpu for budget 6 core.
and it would be able to play overwatch and destiny (and have much the same problem streaming )
hope this helped
Ryzen 5 2200g is a quad core with no SMT. The lowest end 6 core in the lineup for 2nd gen is the Ryzen 5 2600 which has 6 cores / 12 threads. The Ryzen 5 2600 is good for live streaming on a budget.