What are your present countertops? In general, a good company will know what they are doing and warn you of any potential problem.

We removed our ugly quartzite countertops ourselves a couple of months ago. We took off all the drawers and door fronts first. Then sliced the silicon which was used as an adhesive. If yours are stuck on with silicon, I wouldn't be too worried about removing them. If some other adhesive was used it could turn out badly. After slicing the silicon we were able to lift them off without causing any damage. Our boxes are plywood and not particle board, but they held up without any problems.

Is there a backsplash? If so, it will likely be damaged with the counter removal. The wall behind the backsplash could also be damaged. The floor can be trashed by little bits a grit so be sure it is carefully covered.

Will the cabinets be sturdy enough for the weight of the new counter?

I wouldn't worry about damaging cabinets. Slide a Japanese pull saw between the cabinets and stone to cut any adhesive. I never guarantee backsplash against damage when I pull tops.

The other thing to consider is the age/condition of the existing cabinets. If you plan to install stone countertops of some sort, their life expectancy is many years, many. If your current cabinets are already middle-aged or early dotage, will you be happy with your kitchen in 5 years? 10 years? Alternatively, if your cabinets are new-ish and you just don't like the current countertops, then go for it.