No. Fallout 4 is a CPU dependent game. Watch the performance review below.
Joker Productions: Fallout 4 PC Performance Review | 980 Ti, R9 380, 970 Tested
https://www.youtube.com/watch?v=F5ojEukUj94&t=5s
Were it me, the minimum I would do is sell the i3-2120 used on Ebay for $30 and buy a i5-2500 on Ebay for $60. I would also sell the Asus r9 270x for $90 and buy a EVGA SC Gaming 6GB for $270 on NewEgg. That's what I would do if I had $300 to spend. If not then I would spend the $30 difference to upgrade the CPU. There will still be a bottleneck but the sandy bridge i5-2500 is 50-60% faster than you i3. Every bit helps.
Addendum: If you buy a new GPU, then keep the vendor and shipping boxes. There is a chance that the GPU may not work initially but if so, then you can upgrade the BIOS and chipset of your motherboard. Most likely it'll work fine. Another option is you could spend $300 to upgrade your platform to a kaby lake i5-7600k and keep your graphics card. Since you didn't mention a desire to upgrade or a potential budget, I'm just throwing a bunch of ideas at you.