So far as I know the answer is no. A taxi will always be a taxi and a police vehicle will always be a police vehicle. You can replace them with other things and the game will still function fine, but when it comes to taxi and police the vehicles will always be seen as what they were originally cast to be.
The only exceptions I have found is, you can change a two door vehicle to four doors and vice versa, and you can change motorbikes, forklift, airtug, ripley to cars... change engine sounds. Still haven't seen anyone change a non-cop vehicle into a cop car.