As long as the participant made an elective deferral equal to at least the catch-up ($5,500 for 2014), then yes, they can be provided the entire $57,500.
Meaning, it is not just the 402(g) limit or ADP test failure that creates a "catch-up" deferral.
If the plan limited regular deferrals for HCEs to 5% of compensation, they could still defer 5% of pay plus $5,500 (but they can't defer more than their wages, of course).
In your case, deferrals get classified as catch-ups due to the 415 limitation. If the combined ER and EE allocations are enough to push the total allocation over the $52,000 limit for 2014, then deferrrals are classified as "catch-up" deferrals as needed up to the $5,500 limit.
Of course, as you noted, all other testing still has to pass: 410(b), 401(a)(4), etc.
I have not yet seen a document that would not allow this, but double check your plan language just in case. For example, it should say something like this:
Catch-Up Deferral. A catch-up deferral is an elective deferral by a catch-up eligible participant and which is greater than: (1) a plan limit on elective deferrals; (2) the annual additions limit under section 415(d); (3) the elective deferral limit under section 402(g) or (4) the ADP limit under plan section X.X.