Maybe - but it depends on how the bitrate gets allocated between the I-frames and difference frames.If the codec is weak, it will fall apart as soon as there's a moving subject or some camera motion.
You're assuming the I-frames get allocated quite a lot of the bitrate, leaving the difference frames relatively light. If so, then yes - it will look great on static scenes but show problems with high levels of movement.
But it's possible to reallocate the data - same codec, same overall bitrate - to give more to the difference frames at the expense of the I-frames. That will mean more robustness with motion, but a lower performance with static frames. Robbing Peter to pay Paul.
There's evidence that certainly early implementations of AVC-HD did exactly this. They stood up to high levels of motion well (better than HDV, say) but showed noticeably more artifacting on static scenes. (It was visible on such as uniform gradients as a form of "noise", but which changed at GOP rate (every 1/2 sec) rather than frame rate, as normal video noise.