I want to say no. This is why:
I own a Phenom II X4 945 @ 3.0GHz with a Sapphire 7870 GHz Edition. I game on a 32" HDTV @ 1360x768 resolution.
I can play BF4 on Ultra no problem. The X4 955 is faster and better than the X4 945. The 270 is also faster than the 7870 supposedly. I've seen videos of people with the X4 955 and 270 playing BF4 on Ultra @ 1080p w/ 30FPS+
You shouldn't have a bottleneck. :]
EDIT: Got ninja'd by Gam3r01. I don't know why you'd say it will bottleneck at lower speeds? I can play every game except Arma 2/3 in multiplayer(not my fault, bad optimization), Borderlands 2(last time I checked it just lagged the whole time, could be a wrong setting), and that's about it. Planetside 2 and BF4 work wonderfully on Ultra. So why would a X4 945 w/ 7870 not bottleneck while a X4 955 w/ 270 bottleneck? I don't understand.