不是,因為前面是一個很明顯的時間狀語從句
本句變成She hearing the news, tears came to her eyes. 就是獨立主格了
獨立主格表示時間是這樣的
Night coming on, we put ourselves up in a small hotel. 夜幕降臨,我們在一家小旅館住了下來.
（= When night came on, we put ourselves up in a small hotel.）
All the guests seated, they began their dinner.
所有的客人就坐后,他們才開始吃飯.
（= When all the guests were seated, they began their dinner.）
With everything she needed bought, Grace took a taxi home.
所需要的都買好后,格雷斯打的回家了.
（After everything she needed was bought, Grace took a taxi home.）