Yes, it can cause a lot of problems, beyond just kicking up silt.
There is an inherent upward thrust with the flutter kick. While it is propelling you forward, the upward thrust on the "down cycle" has a great tendency to push the diver up as well. That's why many divers achieve neutral buoyancy when they are kicking, but when they stop, they start to sink.
If you're in trim, the effect isn't so great, but if you're out of trim (plow position), your kicks will now propel you up and forward as your body is in a diagonal attitude, facing up and forward.