Yes, a GT1030 can run CSGO pretty well, but mostly because it's more CPU-dependent than anything to do with the 1030.
The A6-7400K isn't a strong CPU to begin with, with the benefits (mostly) being the onboard GPU.
By using a discreet GPU (assuming you've connected the display to the GPU and not to the motherboard), all you're doing is not using the onboard GPU.
It doesn't miraculously improve the CPU performance, unfortunately.
What resolution/settings are you playing at? Are you monitoring your CPU/GPU/RAM utilization?
If not, something like HWMonitor can do that for you:
https://www.cpuid.com/softwares/hwmonitor.html