Can H264 achieve "equivalence" with ProRes 422?
Well going by the numbers h264 has a lesser bit-depth and color accuracy than ProRes 422. PR422 has 10bit and 4:2:2 chroma sub-sampling, h264 has 8bit and 4:2:0 unless you encode in the Hi422P Intra profile which isn't very well supported in the wild but offers 10bit and 4:2:2.
So in that case I don't think you will have any difference what so ever between the two formats but a better compression ratio than with ProRes.

E: If you want to go real ape shit you can also encode in the 4:4:4 Intra Profile, that supports up to 14 bit of color depth. So technically superior to ProRes4444. Though you probably wont find any commercial application that supports it.

On another note, I don't think content delivery for cinema should be done in h264 nor ProRes 422 especially when you plan to encode to a lossless codec (JPEG2000/DCP) afterwards. It just doesn't make much sense to do so, all you loose is quality even though there is no need to do so, you only save space until you encode your DCP. There are other good lossless codecs, that offer very good compression, to use before encoding the DCP.

You could for example go directly to DCP, the Adobe Media Encoder offers export to 2k DCP since CC 2014, you can skip an encoding step and have a lossless codec with very good compression ratio.

Another great intermediate codec is UtVideo aswell as Schrödinger (an implementation of the Dirac codec from BBC, its available through FFmpeg).

In the end though theory always differs from practice and if you don't deliver for nation wide cinemas with excellent projectors and what not, that quality difference in your delivery chain will be neglectable.
The only thing that could be pitfall is that h264 is very complex an by that always prone for some weird visual defects, so final inspection is always a necessity with h264.