I've never tried to make global constraints, but I can tell you that if you want to mark a field as not blank and not nullable you don't need to create a new constraint at all, just add this to your domain class:
static constraints = {
    email(blank:false)
}
Of course if you're expecting an exception on save you won't get one - you need to test the object after calling save() or validate() as demonstrated in this domain class:
class Contact {
    static constraints = {
        name(blank:false)
    }
    String name
}
and its test case:
import grails.test.*
class ContactTests extends GrailsUnitTestCase {
    protected void setUp() {
        super.setUp()
    }
    protected void tearDown() {
        super.tearDown()
    }
    void testNameConstraintNotNullable() {
        mockDomain Contact
        def contact = new Contact()
        contact.save()
        assertTrue contact.hasErrors()
        assertEquals "nullable", contact.errors["name"]
    }
}
If you do want exceptions on save, you can add this setting in your Config.groovy:
grails.gorm.save.failOnError = true
I found it to be quite useful in development.
HTH
PS
To use a constraint you've defined you'd need to add this to your domain class:
static constraints = {
    email(shared:"myConstraintName")
}
But be warned, you can't test the constraint in a unit test as you would the built in ones as the config will not have been read.