It could hurt you if it’s your only math on the transcript and you applied to UCSB. They want to see a math grade (even remedial) by fall. However, if you are denied admission, I have heard of a few successful appeals after the course is completed.
You also need it completed by fall for any TAG.
Lastly, while most majors/UCs accept it in spring, it’s one of those courses that can occasionally be problematic in spring, depending on major and the overall inclination of the admissions office. Sometimes they will have a requirement of a B grade in the provisional, if accepted, so keep that in mind.