Hmmm no, it wouldn't be cluttered with debris, and yes, it's a good idea to park the JWST (James Webb Space Telescope) at the Sun-Earth L2 point.
The five Lagrange points are unstable, for one because of the gravitational anomalies of the two massive bodies of the Lagrange system, eccentric orbits, and there are many other factors to their instability. At the same time, they are least gravitationally attractive points around two massive bodies.
Think of L-points as parking your car on a flat space at the top of the hill. You'll have to approach with some control and then try to balance at your parking spot, if you don't plan using your handbrake and also remain there stationary:
Visualisation of the relationship between two massive bodies and their five Lagrange points (Source: Wikipedia)
There wouldn't be any debris clutter there, or any other matter like smaller particles, at least not any more likely than elsewhere around them, only transient in nature and possibly even less likely than elsewhere since all the other mass particles would gravitate towards the more massive bodies of two Lagrange system centers in their vicinity.
No body with rest mass would stay there on its own accord, not unless it has active attitude control to position itself there and constantly adjust for changes in gravitational attraction vector as the two mass bodies rotate around their axes, change distance while orbiting each other, or L points being influenced by other mass bodies of the same planetary system.
At the same time, JWST will be shielded by the Earth from any Solar activities and also Sun's interference with JWST's sensitive equipment as it starts observing the Universe in the infrared spectrum. Most of the orbital debris from our own space exploration missions is cluttered in the LEO (Low Earth Orbit) belt at roughly an altitude of 500-1500 km above the Earth's surface:
Source: Active Debris Removal: EDDE, the ElectroDynamic Debris Eliminator, Jerome Pearson et al. (PDF)
Now, the JWST will be deployed to a very large 800,000 kilometres (500,000 mi) radius halo orbit around the Sun-Earth L2 point, that is 1,500,000 kilometers (930,000 mi) from the Earth, around 4 times farther than the distance between the Earth to the Moon. So not exactly in Earth's shadow and it will still use large deployable sunshield, but that's a long way away from where we're littering our LEO or even GEO/GSO (Geostationary/Geosynchronous orbits) with GEO being the farthest of these frequently used orbits, at 35,786 kilometres (22,236 mi) above the Earth's equator (and its graveyard orbit a bit farther than that). JWST will be placed in halo orbit nearly 40 times as distant from the Earth as you'd expect any space debris cluttering our planet's orbits at.
Yes, it is a very good idea to place JWST around the Sun-Earth L2 point.