Technically it is possible.
The attached document has a style "WithHyphenation" with the attribute
fo:hyphenate="true" and a style "NoHyphenation" with the attribute
Apply one or the other style to a text box will turn hyphenation on/off.
The problem is in the UI:
The icon of command "Hyphenation" does not follow on/off in its state.
There exists no option, to remove the direct paragraph style on the content
text, if you have set it by any operation.
I have edit the file itself to remove the unwanted direct paragraph style on
the content text.