For isolated singularities, the answer is **no**.

In fact, it follows by a result of Elkik that any deformation of an isolated singularity is algebraizable. See

R. Elkik, *[Solutions d'équations à coefficients dans un anneau hensélien][1]*, Ann. Sci. Ecole Norm. Sup. **6** (1973), 553-603,

in particular Part IV.

  [1]: https://eudml.org/doc/81927