Hope can copy mutant abilities, while Rogue steals them (albeit temporarily). If Rogue has a collection of stolen/borrowed abilities and Hope copies her, does she get the collected abilities or just Rogue's power to steal others' powers? Or do their powers interact in some other way altogether?
Hope's primary power is to mimic the genes of mutants around her. If she was close to Rogue, she would mimic her ability to absorb mutant powers (an ability she doesn't really need), but unless Rogue's genes are temporarely altered when Rogue absorbs the powers of another, there is no reason to think Hope would gain any additional powers from Rogue.
Hope and Rogue may actually be opposites, given that Rogue's powers do not work against Hope. Hope's power over Rogue appears to be something of a cancelling nature (immunity and reduction).
She also proved to be immune to Rogue's newly lethal absorption power and her touch erased all of the previous memories and abilities Rogue had absorbed, including those of the Hecatomb. She also cured Rogue of the Strain 88 virus. (wikipedia)