Yes, she was. Even Sita and her sisters all were warrior princess. As when Shri Ram was informing her about he is going to forest and the way and reasons maa sita gives to Shri Ram is a must be listened to or read.
None of the princesses in either era was a damsel in distress. Even Sabri the way she is shown in valmiki Ramayan . She was no damsel in distress when Matang Rishi took her as his shishya.
There is one spiritual teacher who uses this as a reference to teach or inspire girls learn martial arts for her own safety for this day and age.
I have read some stories - not sure if they were from any particular versions of Ramayan or if they were folk tales. Shabhari was the daughter of a hunter but she had a very kind heart. When her wedding was arranged she didn't want many animals/birds to be killed for wedding feast via hunting sprees. She objected to this but her views weren't accepted. So she left her tribe and sought guidance from the sages in the forest. Nobody wanted to accept a hunter woman as his disciple. Only sage Matanga accepted her. The others were not happy and hurled insults at them both but Matanga continued to tutor Sabari. When Rama visited the place, the sages complained that the lake Pampa nearby is unusable because it's waters have turned red and it's full of worms and asked if something can be done about it. Lakshman says this was due to the insults they hurled at Matanga and Shabhari. Rama says if Shabhari can take a dip in the water it will become clean again. Nobody had the courage to ask her and when Rama asked her if she would do it, she gladly accepted and said if it was for the good of people, she would do anything. She went to the water and the moment her body entered, the water started clearing up around her. When she took a dip and emerged back, the water became crystal clear and usable again. This everyone respected her afterwards.
This story seems a bit too fanciful to me. Firstly, her escaping her wedding seems similar to Sidhartha (Buddha) and the later part seems similar to stories about Vaishnavaite devotees like Eknath. Secondly, in Valmiki Ramayan, Rama asks her about her Gurus and she gives an explanation - a part of Valmiki Ramayan that I still don't understand fully. Shabhari was to wait there for Ram and She doesn't sound like someone who was made an outcast...
The incident could have happened and may not have happened. I have no idea.

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