Sadly seems like it's way too small.
Pioneer 10 is ~2.9m long [1] and 2.0e7 km from Earth [2]. JWST is just 1.5e6 km from Earth, so that doesn't make much of a difference.
Doing the trig, you get the arc-width of P10 is 2atan(w/2d) = 2atan(2.9m/4.0e7km) = 7.33e-14 rad.
JWST has a resolution of 0.1 arcsecond = 4.8e-7 rad [3].
So we're off by "just" a factor of 10,000,000 on resolution :-(