I can only contribute what I know from my recent United Mileage Explorer and CSP approvals.
Chase will randomly pull any of the 3 bureaus. However, if they try to pull one and it is frozen, you just need to call the backdoor number. An analyst can pull any of the 3 on the spot! (I speak from personal experience. Chase manually pulled TU for the United card and EQ for the CSP after I called them.)
Hope this helps!
Starting scores: Around 630 (Sep 2011)
Current FICO scores: TU ‘08 792 (Walmart) • EQ 765 • EX 771 (Amex)
Prime cards: JP Morgan Select (30K) • HHonors Reserve (30K) • Chase United MileagePlus Explorer (20K) • Chase Sapphire Preferred (20K) • Amex Hilton Honors Surpass (20K) • Amex BCP (20K) • Barclay Ring (20K) • Citi Thank You Premier MC/Visa (16K Combined) • Discover Escape (10K) • Amex SPG (5K) • Amex Premier Rewards Gold • US Bank Cash+ (5K+???)
Starting Score: 617 EQ 10-17-11