Your question is a bit vague so i'll try to cover several ideas (email me with more specific info for a concise conclusion).
Is the tree young, well established or in maturity? What species of cherry is it? Was it healthy or in a weakened state? Some species are more resilient, others (most ornamental flowering cherries) are prone to every airborne pathogen under the sun. The answer will vary according to each case. When you say 'right down' do you mean to the stump, just a few inches off the ground? If this is the case with an older specimen then the answer is most assuredly, no. That's not to say you couldn't try to propagate a new shoot from a root cutting... not the same thing really, but better then no tree at all.
If all foliar coverage has been removed, there are no leaves to photosynthesize and no sugars can be produced to sustain the tree. Adventitious buds might sprout but will ultimately not produce enough foliage to sustain a fully developed tree. Based on my professional experience to date I have never witnessed a mature cherry sprout adventitious buds after it has been cut right down.
If the tree is still a sapling or quite young, adventitious growth may well be enough to re-establish a healthy new body of foliage.
If on the other hand you meant your cherry has been 'severely pruned' as opposed to cut right down, the answer is: it may recover assuming it was not previously in a state of stress. If it does, it will probably be in a weakened state due to excessive pruning, but may well survive and in time return to health.
When pruning a cherry (and many other deciduous species) you should try not to remove more then 30% of the foliage producing part of the plant to avoid inflicting undue stress. Pruning should also ideally take place after Autumn and before Spring for optimal results.
These are ideas based on my own experiences in the field. As you haven't included several details I'd consider necessary to accurately determine the likelihood of recovery, I can't give you a conclusive answer. I feel the outlook may not be so hot but, I might have completely misinterpreted your question.
Feel free to email me with additional details/photos if you want a more accurate assessment of the situation.
5 years in arboriculture and the tree care industry.