No, the Hubble cannot resolve even the largest pieces of Apollo equipment left on the Moon - not even close.
Keep in mind that there is a difference between resolving and detecting an object. For example - we can
see the stars with our naked eyes - but even the world's biggest telescopes have trouble resolving some of the closer/larger ones into disks.
As a final thought - even if Hubble COULD detect the Apollo equipment, I doubt anyone would see it as a good use of its time. And keep in mind that conspiracy theorists have been denying the mountains of evidence in favour of the moon landings for ages - they would just turn around claim that the Hubble pictures are fake too, or that the equipment was placed by unmanned means. We already have images of the Apollo's 11 and 15 landing sites taken by Clementine and Selene that show the diffuse surface disturbance due to the LMs descent/ascent - but nope, that doesn't count for the conspiracy theorists.