My first thought would be no, but then with a quick second thought, possibly it could regenerate depending on the drying procedure and/or kind of plant. For example, if you dried some cacti or even a chunk of one it would at least in some cases grow again if re-hydrated and/or planted with water. Likewise, a single leaf of say mother-in-law's tongue (Sansevieria spp.) --quite long and thickish -- might well survive drying if meristematic tissue at its base remained undamaged and with re-hydration could grow anew. I'm sure this is possible.

In my only experiment years ago with a somewhat parallel instance, we removed small seeds (from their capsules) on pressed herbarium specimens of desert plants long dried in our collection (ranging from 10-20 years). Quite a number germinated in culture media and I was able to complete chromosomal studies using cells from growing embryonic tissue. Clearly the seeds had adapted to drought conditions in their desert environment and remained dormant even when (we thought) totally dried out as part of our preparation for museum deposit. We never examined how much hydration existed in the seeds, but I suppose clearly some moisture was there for the slowed down metabolism to allow for the dormant seeds to remain viable, rehydrate and grow.