Distance to the target doesn’t matter because to an astronomical telescope every object of interest is at optical infinity, but yes, if you know (an approximation) of the optical system’s point spread function, you can compensate for the effects of aberrations including diffraction.

The JWST team knows the PSF from having designed, simulated, and now actually testing the telescope, and likely it will come useful in getting the last bits of scientifically valuable information out of the data, but in normal use those diffraction spikes in particular are unlikely to be any problem. They basically only show up because the star in the test image is highly overexposed.