There is a paper which actually discusses in great detail the history of the selection process, which can be found at the SWRI site, at least for the New Horizon mission opportunity. Let me sum it down as below.
There were 3 majorly competing proposals for the Pluto Kuiper Belt (PKB) mission. One of these included an ion engine, which was not selected. It is possible that such a mission could have reached Pluto even faster, but it does take up valuable mass. The entire spacecraft only has 400 Kg of mass, and even a modest sized ion engine with a tank would eat into that budget significantly.
The current record for speed change is held by the Dawn mission. I don't have an exact figure, but this article says it's expected total velocity change is 38,620 km/hour. This article states that New Horizons is 57600 km/hour. I can't find the velocity of Dawn as it escaped Earth, but it was definitely less than NH.
For all of this great change that Dawn had, it requires significant extra mass, as can further be seen here. Dawn was one of the heaviest spacecraft ever launched.
The time from announcement to launch was also an extra year. The announcement for Dawn was on Dec 21, 2001, launch was September 27, 2007. New Horizons was announce in 2001, launched on January 19, 2006, thus it had 18 months less. The deadline to launch New Horizon's was very firm as well.
So, putting all of this together, it is possible that a mission to Pluto would be faster than a conventional mission, although not extensively faster, but it would have cost more, and probably taken longer to launch, and added extra risk. But with Dawn's success, missions like this will be more possible in the future.