I think it depends on the company on both counts. With many companies leaning towards online applications you will most likely have to mail them in after an initial application online, or bring them with you to the interview. If possible, I would mail them in at the earliest opportunity (unless directed otherwise, but not with the initial cover letter and resume, I mean after the app has been sent in or with it) and also take copies with you to the interview.
A couple of years ago SW required 3 LORs from anybody who could attest to your flying ability. I think everybody feels that letters coming from pilots who work for the company you are applying to are best, but I still think its good for potential employers to see that your current superviser thinks enough of you to write a letter as well. I used 2 LORs from SWA pilots and one from my supervisor at the time. If you don't know anybody at the airline, send in what you can from those who you fly with now. The more recent, obviously, the better.
Once everybody goes to an online app process I think they will have pretty explicit instructions on how and when to handle LORs.
