Yes you can natively edit with h.264 in FCPX. But the nice thing about FCPX you can import your footage and transcode your material to; optimise and proxy (in the background) then you just switch between the different formats with a click with no relinking.
But back to your question I would do a test if you see a difference in transcoding your footage in ProRes and downscaling it... in FCP7 or your transcoding tool of choice.
So your delivery is 1080, do you even need to edit with 4K material (punch in..)? It always good if you ca offered a step less in a workflow.
Following are the requirements to edit 4K with FCP
The following Mac computers are capable of viewing 4K resolution via HDMI from Final Cut Pro X 10.1.
Mac Pro (Late 2013)
MacBook Pro (Retina, Late 2013 and later)
The supported 4K resolutions are as follows. Note that not every 4K monitor will support both of these resolutions, and 4096 x 2160 is only supported via HDMI at 24fps.
4096 x 2160
3840 x 2160