I think a healthy body could survive a single instantaneous disappearance of current mRNA, as long as the mechanisms to create more mRNA remain functional. All cells would just respond to new conditions more slowly and less effectively for a few minutes to hours, leaving the body vulnerable to disbalancing conditions such as infections. Some cells would die but most of them can be replaced in days.

On the other hand, deleting DNA (and thus preventing the creation of RNA) cannot be survived. A great exploration of such scenario is in the No More DNA chapter in What If? by Randall Munroe: the syptoms would be like eating an Amanita mushroom such as the "Destroying Angel", whose amatoxin prevents DNA transcription, or acute gamma irradiation. The patient is fine for a few hours (or less with a theoretical DNA wipe), then start exhibiting cholera-like symptoms (vomiting, abdominal pain, diarrhea), then they start to feel better. However, at that point, since cells can't divide, immune system collapse or systemwide organ failure is inevitable.