It is possible to do it by tourist train in one long day which would be better than not seeing it at all but it really deserves more time. We traveled by train from Cusco to Puno. This was a serious mistake in our opinion. The trip takes 10 hours and it is very dusty and uncomfortable. There is some interesting scenery for about 4 hours out of this 10 hours trip.
Rooms are small, dark, cold, and uncomfortable.
The staff is very rude. A most unpleasant experience in our opinion. We then went by hydrofoil across Lake Titicaca to Huatajata. This was a most interesting trip and is recommended. This was a mistake.