That's a very good question, Felis. Using windows, the edit boxes are directly editable, but with iOS and Android mobiles, getting input from edit boxes calls up the GetTextInput routine, which is limited to "characters in the ASCII range 32-126."
But to completely test, an extended font image is needed, and I don't have one handy. Do you have one we could test with?
EDIT:
Here's a test that seems to indicate the text box can display extended characters, at least with the default AppGameKit font.
testText = CreateText("")
for x = 128 to 256
a$ = a$ + chr(x)
next x
SetTextString(testText, a$)
SetTextMaxWidth(testText, 100)
CreateEditBox(1)
SetEditBoxPosition(1, 0, 20)
SetEditBoxText(1, a$)
SetEditBoxSize(1, 100, 50)
SetEditBoxTextSize(1, 5)
SetEditBoxMultiline(1, 1)
do
Sync()
loop
