Not with "save as a clone"
It's often useful to set up a script that initializes all global fields with expected default values for each. You can then run this script after the save a clone operation in the new copy to set the desired values. This doesn't work if the global field is a container field in many cases.
You can also save a regular copy of your database and then delete all records in the copy. This can take a while in large files with millions of records but your global field values can be retained this way.
Thanks Phil, that confirms my thinking. Good answer. -DJ