Probably not.

Some years ago, astronomers at the Naval Observatory constructed a computer called the 'Digital Orrery' which calculated the positions of the outer planets every 40 days or so, for the next billion years.

Even though the orbits of Pluto and Neptune intersect, they are locked in a gravitational resonance condition which seems to prevent them coming closer than a few 100 million miles of one another. The above computer simulation of thousands of Pluto orbits is made relative to a frame or reference that orbits with Neptune. It shows that although Pluto's orbit is complex, it can never get very close to Neptune itself because of the detailed ways in which energy is transferred between the planets, gravitationally.

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