Of course, for monogenic diseases, of which there are many.
For complex diseases that are dictated by complex interactions between 'gene X environment', we can perhaps only produce a probability of having a disease or developing it within a specified time-frame, e.g., risk of developing cancer by age 55.
Lets me take a look at your question in a bit different view than what Kevin did:
It depends on what do you mean by SNP:
By SNP if you mean those single nucleotide variants that are present in a relatively large fraction of the population ( > 1%), the answer is a big NO! These markers are useful for doing genetic association studies. In these studies, researchers only investigate to see whether there is an association between a genotype and phenotype or not. Here the study can not say anything about causation of the variant with regard to the phenotype development. Indeed the result of association studies has no clinical utility and so genotyping for common SNPs (even those showed a very strong association with a phenotype in GWAS) should be avoided to be offered to patients.
For diagnosis, it is mandatory to know how relevant is the variant to the observed phenotype. Actually in diagnosis causation matters. For example, consider the rs33915217 variant. However by definition, it has rs# (comes from dbSNP) and considered to be an SNP, but it can CAUSES Beta Thalassemia ( a Mendelian disorder) as recorded in the ClinVar database (https://www.ncbi.nlm.nih.gov/clinvar/variation/15447/).