If the virus-carrying mites are still present in the soil where an RRD infected rose was removed, and a replacement rose is placed in the same spot, then yes, I think the mites could infect the new rose.
Whether or not you replace the rose, you may want to consider using a miticide. However, some miticides known to control spider mites do not necessarily control eriophyid mites that transmit RRD. Some of the miticides that are registered for controling both eriophyid and spider mites include:
Avid
Talstar (bifentrhin)
Sevin (carbaryl)
Thionex and Phaser (endosulfan)
Petroleum-based horticultural oils (don't apply during high temperatures)
