AFAIK, it's not possible to change the manual editing workflow to "select one of the domain codes or type in your own value".
But you can insert features with "wrong" values using Python (and probably Arcade, though I haven't tested that):
with arcpy.da.InsertCursor("Table", ["Field"]) as cursor:
cursor.insertRow([5]) # Coded Value Domain [0, 1]
Have a great day!
Johannes