Is Quicktime required for After Effects and Premiere?

You only need the quicktime components. Not sure if you can remove them as they ar part of the OS. Also, as suggested by @Jqke , H264 is a heavily compressed format, not the best way to work on professional environments. Your machine will need some CPU/GPU cycles to decompress H264 before playback and your workflow speed will be affected. 

I always use H.264, it works the best for me. But AE has lots of codecs you can render in, so you should be fine? Let me know if I understand your question correctly or not.