Yes, you can do this with arcpy. I usually use arcpy.da.ListDomains to iterate through the domains but in your case you just need to see if there are any domains assigned to a field in feature classes. This code can iterate really quickly through multiple feature classes and report those that have a field that has been assigned to the domain you've specified.
gdb = r"C:\GIS\SDE_DB_CURRENT_SNAPSHOT.gdb" #supply the geodatabase path
arcpy.env.workspace = gdb
domain_to_search = r"CodedValuesCountries" #supply the CV domain name
fcs_list = arcpy.ListFeatureClasses()
for fc in fcs_list:
fc_fields = arcpy.ListFields(fc)
for field in fc_fields:
if field.domain == domain_to_search:
print "feature class that uses this domain is", fc
This code can be run from Python window in ArcGIS, as a script tool or from an IDLE or IDE such as PyScripter.