No, the plugin doesn’t support that field, but only because no one has ever asked for it before. I think it’s usually just set globally in the ‘discussion’ settings. Does your blog require it on an individual post level?
I noticed the field in the table and most of my manual post state open for ping status. I noticed on my turbo imports it sets it to closed if it is a draft and open if it is publish. After looking into this further it seems controlling it as open and closed might help since closed can prevent trackback spam. Just an FYI, I think when you change the setting in discussing settings it only updates new post to this status, not existing posts.