Wait, that's not exactly what I said (or at least not what I meant). I think two separate issues/answers are getting mixed up here.
The first issue is: my application is incomplete because I am missing something (like LOR's). Should I apply now or will my application get passed over?
In this case, there is no harm to applying now. Your application will be downloaded now. Programs create "filters" to look for complete applications -- each program can define a complete application any way they want. If your application does not meet their definition for complete, it will simply sit in their application system until it does. As soon as the missing information is downloaded and your application meets their definition of complete, it will appear the next time they query the system for complete applications. Hence, in this situation, there is no harm to applying early.
The second issue is: my application is basically complete. However, I am expecting some additional piece of information -- perhaps Step 2, or a fourth LOR, or AOA status. I think that this remaining piece of information will make a big difference to my application. If I apply now, could I possibly be rejected before this information has been received, and then if it comes in later will anyone notice?
The answer to this is different. Most programs do not consider step 2 to be necessary for "completion", since many AMG's will not have Step 2 prior to ranking. Hence, it is very possible that your application could be reviewed before your step 2 comes in, and you certainly can be rejected. Once you are rejected, your application is marked as "inactive". Although additional information will continue to be downloaded from the ERAS post office (such as your step 2 score), the application will no longer be reviewed unless the PD/PA runs a query asking about inactive applications. Hence, this situation is different. If you are waiting on a vital piece of information -- Step 2, and LOR, or AOA would be the ones that come to mind -- you might well be better off waiting until that result comes in.
You can always ask to be reconsidered once a new piece of information becomes available. Some programs will do so, some will not. We get 100's of applications per spot, re-reviewing one's we have rejected already is not fun.
Sorry for any confusion.