The ATP Certificate Training Program must be completed before you can take the ATM written test which is the written for a multi-engine ATP. It does almost nothing to prepare students for the written test. You will have to do some studying on your own for the written. The CTP is designed to fill the "knowledge gap" between single engine CFIs and regional jet F/Os. But the FAA says everyone must complete the course. I've felt bad for Air Force test pilots having to sit through 8 hours of aerodynamics. Many of the CTP providers (ATP, CAE, Pan Am, etc.) are Part 142 schools and can conduct the checkride for an A320 type rating. However for the type rating you would have to complete aircraft GS and flight training before the checkride. The CTP and the ATP checkride are separate events. Or you could complete the CTP, pass the written, get a medical, thrash around a few hours in a light twin and get the ATP ME without a type.
Not plugged into the hiring side but as I understand it the Big 3 are committed to their flow programs and so street hires are done when there are not enough flow candidates. Most major airline hires the last few years have been through the flow programs. Brown and Purple don't have as many flow pilots so most of their hiring is off the street.