Does joint compound or ceiling texture emit a harmful odor?
Before reading your question, I would have said that joint compound is completely inert/ non-toxic/ ready-to-serve. (That last one was a joke, btw.)

Looking at a couple of MSDS sheets for common joint compounds, they seem pretty inert. However, there are suggestions on the interwebs (for all that's worth!) that some joint compounds contain traces of vinyl acetate monomer, acetaldehyde and formaldehyde. 

My best suggestion is to request the name of the actual products used, and seek out the MSDS sheets for those products. It's possible that she is sensitive to something in the mix. Having said that, though, these things usually off-gas pretty quickly... ventilating will do a world of good.

If a popcorn/stucco touchup is next, there are a few types of product used, but most common are canned (aerosol) wall texture, and premixed/powdered wall texture that are sprayed on with special equipment. If they opt for something in an aerosol can, you might want to specifically request that they use the water-based version, as oil-based ones are smelly. The spray-on ones are probably as inert as the joint compound used for patching.

If there's respiratory sensitivity due to dust, be aware that sanding drywall is messy and it's either that extreme dust containment is needed, or that your grandmother might choose to leave while work is being done. 

Same sort of advice for painting: request low VOC paint (which is quite typical these days), ventilate, or vacate.