'Their' licences are FAA licenses just like all the other flight schools and no flight school in the US can get you a preferential interview with Delta mainline. All you can do is get your licences, work up your experience and then get enough PIC/turbine/whatever the competitive requirements are for the airline you'd like to work for then send in your resume like everyone else. You will not get a shoe in anywhere unless you have someone on the inside who can give you a recommendation. Often you need several.
Airlines here do not hire 250hr pilots. You'll also need a greencard or citizenship and, as someone mentioned, a degree is often necessary for a major. Good news is that most do not require you to pay for your own type and the CRM training is in house.
I would not recommend the Delta Connection Academy.
Please do some serious research first and check out all the different places/prices available in the US! Often it's easily as quick to go to a smaller flight school, get your ratings with the same instructor all the way through, work as a CFI (if you can get work) and then send your resume out when the job situation has improved.