Yes and no - there is no tool that does this fully automatic - you have to set up and tweak the chain your self, but once you're done it can be used with any input (i.e. "live").
(tl;dr: good impersonation -> pitch-shift w. formant control -> matching eq)
Like you suggest yourself in one of the comments, you have to use a mix of both a good pitch shifter (pitch correct) with formant control and an EQ that allow you to sample the profile of another sample.
If you use a simple pitch shifter it will not sound natural - the formant control is important:
Besides Melodyne, there is the Pitch Correct plugin in Cubase (not VariAudio as there is no formant control) and a free one: MAutoPitch
By ear, set the pitch shift and formant as close as possible to the wanted sound.
Now put on a profile matching EQ, e.g. Steinbergs "Match EQ" or Izotope Ozone Matching Eq and "learn" it profile of the wanted sound and use that to give it the final touch. Here is the trick explained in way too many words ;-)
In this discussion about the video and process, they mention the following plugins/tools: MAutoEqualizer, ReaFir (in subtract mode) and Voxengo Curve EQ.
Now you should have a set up that allow you to process any signal. The only thing left is a good impersonation with typical phrases and words of that person ;-)