Sorry, but you couldn't be more wrong. The draw has followed the same pattern for the 50 years I've been supporting Saints and, I dare say, many years before that.
Rounds 4, 5, Q/F and S/F are drawn on the order your match came out in the previous round. We were 7th out of 8 for the 5th rd, so Sunderland were no.7.
Round 3 has the 2 top division clubs in alphabetical order. We are usually about no.35. Then all the sides that won rd.2, are numbered 45-64 depending on the order they were drawn in rd. 2.