This is all under the assumption that you're application is non-contextual.
They will reject you if you get a low TSA S1 (i.e., about bottom 40%) unless you have a very good cGCSE score (i.e., your GCSEs were good compared to your school's average performance in that year). Predicted grades will not affect your chances of shortlisting as long as it is above or equal to the typical offer grade (A*AA). How shortlisting works is if any one part of your application are not up to standard, you will be recommended for deselection (with the only exception being exceptionally good cGCSE can make up for poor TSA and vice versa).
What they don't weigh in for selection is your personal statement and AS grades (if you took them). TSAS2 is weird because they use it to judge the strength of candidates but poor S2 score does not mean an automatic deselection. Everything else: teacher's reference, predicted grades, cGCSE, TSAS1 need to be what they consider good.
All the information here is accurate for 2016 entry, but I doubt they'd have changed the selection criteria.
With interview offers coming in in mere days this probs isn't the most helpful answer, but best of luck!