The mechanism would loft a cloud of particles with a wide range of trajectories through a notoriously uneven gravitational field.
The odds that a sufficient fraction of particles would remain in orbit for long enough to make routine operations in low lunar orbit or on the surface itself seems ... plausible.
And of course, the situation could be compounded by multiple burns and/or at multiple points on the surface, at a somewhat increased cost to the attacker.
Actually, Moon is rather immune to Kessler syndrone due to its bumpy gravity caused by sub-surface mass concentrations.
So Kessler syndrome could certainly develop for a whiley but would be cleaned up rather quickly as all the pulling & pushing of the "rough" gravity converts the orbital speed into heat, until all the fragments impact the surface.
Might be a bit more dangerous on the surface for a while though, with lot of stuff striking it at near orbital speed in an almost horizontal direction. That could ruin your evening stroll quite badly.
IIRC single digit years probably - Apollo missions released a couple sub satellites and missions control was then very surprised when those satellites lost altitude and crashed in a matter of months.
In comparison, there is likely still stuff from the 60s in orbit around Mars, and that's for a body with (thin) atmosphere.
Kessler is a chain reaction. Destruction is caused by secondary effects, i.e. bits of satellites the primary projectile broke hitting targets. This is closer to an area denial weapon: the destruction is caused directly by the debris blown off the surface.
It is also not permanent. The orbits of the debris would intersect the point where they depart, which is pretty close to the engine. Basically the engine would be hitting itself with everything it fired.
Therefore, the logical thing to do is to put it on the correct side of a mountain, to shield the engine. But that would also collect all the debris. So it would generally only be in orbit for one orbit.
(To be honest, I think on any planetary body without an atmosphere, long term everyone is going to have to dig in to the planet, and to a non-trivial degree, too, not least of which is the complete indefensibility of surface installations.)
The expansion of the gas after it leaves the nozzle in vacuum would give the particles an additional kick. I'm not sure if their orbit would still intersect the engine or effectively boost higher.
I left myself some wiggle room in the phrase "where they depart" for that reason. It won't all be a straight line out of the rocket motor or whatever is pushing, because in the first fractions of a second the gasses and the particles can interact and bash each other into slightly different orbits.
However, that will dissipate quickly and you'll certainly be looking at a set of orbits that all pass through something relatively close to the origin. They're not going to be interacting for the first time a quarter of the way through the orbit and bouncing around a lot there.
