Correction: any Earth-sized planet in another stellar system will most certainly NOT subtend "several pixels"; instead, any such planets will be point sources. In brief, diameter of Earth is around 10^7 m, while the nearest star is of order 10^(16) m away from us. The angular size of the Earth at such a distance would thus be 10^(-9) radians, which corresponds to 0.0002 arcseconds.
In comparison, the diffraction limit of JWST at a wavelength of 2 microns is roughly (2 x 10^(-6) m)/ (6.5 m) = 3 x 10^(-7) radians. That's more an an order of magnitude larger than the angular size of the Earth at the distance to the nearest star; for the great majority of stars -- which are much more distant -- the difference is even larger.
tl;dr JWST will measure Earth-like exoplanets as point sources.