An FAA ATP is an FAA ATP. It matter not one jot how you got to the 1500 hrs - and the sub-accruals - when you come to sitting the flight test.
The requirements for the issue of an FAA ATP do not distinguish between methods to attain the minimum requirements.
The FAA Commercial, however, allows for a credit in the total number of hours required before an FAA Commercial certificate can be issued. The concept is that you can reach a commercial level of skill two ways:
1. Have specifically designed & FAA approved training course where every hour of training, theory & flight, is intended to prepare you to meet the standard, or
2. Do your training any which way - within limits - as long as your skills are up to speed when you do the test.
#1 is the Part 141 system, #2 is via Part 61.
#1 is supposed to be more efficient towards meeting the specific standards for a Commercial while #2 recognises that other experience also contributes towards the skill required, albeit perhaps not as efficiently.
'Not efficiently' isn't necessarily correct however unless every hour is prescribed then it's more problematic to ensure a desirable level of competence - hence more hours required.
Australia has a very similar system WRT to it's 'Commercially trained person' vs 'Non-commercially trained person'. Commercially trained needs a min. of 150 hrs of training, whilst non-commercially trained must have at least 200 hrs of experience.
The UK's equivalent was CAP509 vs (whatever the 'other way' was). That translated under JAR-la-la land to Integrated vs Non-integrated (or is that 'Modular'?). All the same philosphy though.