No. This answer option (one I have never recommended) can mean anything from don't know to don't care to don't understand the question/construct. This numeric imputation can only degrade data quality. Move it out of the scale and depending on the question/audience, be more precise about when/why to use it by using terms like "Not sure," "Not sure yet," "None of these" "Have not tried," or whatever fits best. Don't assign it a numeric value.
Assigning a value to the middle option of a Likert scale is quite acceptable and does not produce unwanted noise in data distribution. However, one should avoid using Likert scales for single questions. If there are multiple questions to the same factor, then the neutral option is balanced out.