Yes and no,
Many of the objects don't need observing at the same time - if we have Hubble data in the UV/Visible on file then observing it in the IR in the future with JWST.
The real mission for JWST is to observe things that are only IR. The early universe with stuff that is now redshifted to being IR, and are too faint for Hubble anyway.
There might be boring nearby, low energy, objects (like planets) that people might want to observe multi-wavelength at the same time, but nobody cares about a bunch of non-cosmologist stamp collectors