For example, if the enzymes in the digestive system stop working will the digestion still occur as enzymes are only catalysts for the reactions.
It depends on what particular enzyme 'stops' working, and what reaction it catalyzes. For one, the human genome (and that of most organisms) has many genes encoding for enzymes with partially (or fully) redundant functions, and this can mitigate the damage to a particular biochemical pathway in the case that an enzyme within the pathway stops working.
That being said, if the reaction facilitated by the particular enzyme is fundamental for the cell/body physiology, then the embryo/organism would not be viable and thus we would not observe these variants. Thus, whenever a mutation with a 'loss of function' phenotype is observed in an organism, it probably is not essential for its existence (although it might affect a lot the proper functioning).
Enzymes accelerate reactions in various orders of magnitude, and therefore, without them, most of the reactions would not occur fast enough to be useful physiologically. So, yeah, they are 'just' catalysts but quite fine-tuned for physiological needs by millions of years of evolution.