Yes it's possible. Use a Field action on the after profile update trigger then set a fields value with the below substitution for example.
[cb:date format="Y-m-d" /]
See the below substitution tutorial for further date substitution usage information.
www.joomlapolis.com/support/tutorials/107-use-cases/18353-using-substitutions-throughout-cb
If necessary you can enable Format Functions under the Parameters tab to use format functions to set the fields value to a date.