Yes. The use of "this" to mean a particular, but unspecified, person or thing is very common, and should be understood by all fluent speakers. Examples might include:
- I found this excellent Thai restaurant -- you should really try it.
- Channel Five has this news anchor who keeps making stupid mistakes.
- The college I attended had this very unusual program.
- In my math course there is this concept I can't seem to understand.
In each case "this" stands for a particular thing or person, but the listener (or reader) is not given sufficient information to fully identify the subject. In some cases the speaker later does provide a name or other details which do identify the subject for which the word "this" stands, in other cases no specific identification is ever made.
For a woman to refer to herself as "this woman", or a man to identify himself as "this man" is very unusual, even abnormal. Sometimes a person intentionally speaks of him- or herself in the third person. This is mostly a literary device, or it is used to suggest the formal patterns of a non-English language in translation, particularly an Asian language. I suspect it is not, in fact, a good translation, but I am not knowledgeable enough to be sure. But even if a person were using third-person to refer to herself as "this woman" (or himself as "this man"), it would not be done in a construction like the one in the question. Instead "this woman" or "this man" is used in place of "I"
This woman needs to tell you something.
This form is used only for limited purposes. I mention it for completeness, and because the question asks if "this woman" might refer to the speaker. I advise a learner not to try to use this form. Confusion and errors are likely.
By the way, the phrase "If a woman say" used in the question is incorrect, it should be "If a woman says" because 'a woman" is singular.