Theoretically, but it would be difficult. As far as vocal tract resonances are concerned, you would have to ‘whiten’ your own voice with a filter that removes your own vocal tract resonances, the filter it with the vocal tract model of the person you want to imitate, including heterodyning it to the correct frequency range. However, there are a number of other characteristics, such as cadence, emphasis, and other factors that would make it very difficult to do easily. You might want to do a PubMed search on speech synthesis to research it in more detail.
It’s definitely not a programming project I would want to undertake!
