Probably not, because for the same reasons that brought down the eastern bloc in the first place, if the USSR was still here, those reasons would probably have stifled development in the space program much like it already did. In the late 60's and 70's, the USSR lost out big time in space exploration and bad support from their political leaders and citizens due to the inability to even match the Americans. Of course, Mir was a great success, it came onto the scene much later when thing were starting to heat up for the communist bloc (around 1986 I believe). But a mission to Mars, I don't think so. If anything, we probably would have started working with the USSR to do a mission to Mars and it would be nice to work with the Russians now on getting a moon base going.