Something like this might work as a workaround:
tell application "QuarkXPress"
tell document 1
set styleList to style of character attributes of style spec "Test" as list
set onStyles to item 2 of styleList
end tell
end tell
I couldn't get the on styles directly. The style "Test" used the "Default" setting for Character Attributes Style, and had Bold, Small Caps, and Superscript checked--all were returned by the script. QXP 6.52.