In theory, yes, possible.
In practice, your cooling will not get big benefit. Reasons for that is mostly that even with separate case, you cannot lower the ambient temperature that comes to radiator that much. Yes, top case might be few degrees cooler due to lacking GPU and such but.. 100% of that temperature difference does NOT translate to cooling liquid, so you would look at 1 to 3 degrees lower temperature at best (on CPU/GPU depending on which the radiators work for)
Is that 1 to 3 degrees big enough difference for such a massive effort? your choice. You would also need to customize the loops to get radiators that far and longer pipes will lower their efficiency too.