Would leakage through a JFET create thermal noise
Jonk's comments are right on the money, so for the most part I'm restating, but also adding a few minor bits.


  Would this be a low noise way of implementing a large impedance?


Nope, in fact it would be modestly worse: 


Thermal noise is \$4kTR\Delta f\$, i.e. thermal noise is directly proportional to the resistance. If you have a large resistance, you have a lot of noise.
...plus a JFET will also give you shot noise as well.
...and last (and perhaps least) a JFET will give you flicker noise (1/f noise) too. At high frequencies you probably won't notice the effect of flicker noise but at lower frequencies it could matter.


A nice overview of these various types of noise in JFETs can be found in this application note (from 1976!).

Bottom line, if your goal is "high impedance with low noise" then you're best off with a plain old resistor, where your only noise is thermal, versus a semiconductor which will introduce these other peculiar types of noise in addition.