不是,因为前面是一个很明显的时间状语从句
本句变成She hearing the news, tears came to her eyes. 就是独立主格了
独立主格表示时间是这样的
Night coming on, we put ourselves up in a small hotel. 夜幕降临,我们在一家小旅馆住了下来.
（= 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,他们才开始吃饭.
（= When all the guests were seated, they began their dinner.）
With everything she needed bought, Grace took a taxi home.
所需要的都买好后,格雷斯打的回家了.
（After everything she needed was bought, Grace took a taxi home.）