What would happen if Rogue touched or was touched by Death (Grim-reaper) ? Would she steal death's power and kill him instead? Seems like it might be a paradox...
No, in the case of an abstract (or cosmic) entity such as Death, it is unlike Rogue will be able to harness any of Death's abilities, mostly because Death does not have a body unless She wants to. For that matter, Death doesn't appear to have any powers, nor does she need them. If she wants you to die, you are dead.
When Death manifests, it is wearing an M-Body, a construct created to allow her to interact with the physical universe. Otherwise she does not have a physical body for Rogue's mutant power to interact with.
For the record, Rogue (Anna Marie) of the X-men has finally gained control of her powers and her ability to absorb the powers of anyone she engages in skin to skin contact. While she is not limited in what kind of powers she can imitate (mutant, mutate, Eternal or Deviant) there is a physical upper limit of power she can replicate effectively.
We have never seen her attempt to take on the abilities of an Omega-Level mutant or a cosmic being such as the Silver Surfer. It is very unlikely an abstract manifestation such as Death would be within her power to replicate.
However, the ability to kill an individual with her power is still within Rogue's realm of capability, by absorbing the psychic/soul/energy of her target.