Technically, yes, you can…but all you are doing is creating a larger file. Depending on your frame rate, you may have some bigger issues too trying to mix.
Use VTR Exchange and set up your source as whatever you are capturing as (frame rate/frame size) 10-bit. Set your compression to AJA Kona 10-bit LOG RGB Codec. This will allow you to capture single link in a LOG RGB codec. Mixing this footage in the timeline in FCP with 2K or 1080p footage is a different story since FCP needs framerate, framesize, and codec to match. If you have all three, voila, no rendering.
Hope that helps.
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-Mike