This year, I've had more people than ever question whether documents arriving separately from applications and other credentials will "make it" into students' files. What makes the questions so surprising is that application components have arrived this way for years and years. Online applications haven't brought this about.
If you apply online, there is absolutely no problem with teachers sending in recommendation letters on their own if they don't want to use our online submission feature. In addition, while it's easy for our staff members to log credentials into the computer system when items for the same applicant arrive together, your guidance/college counseling office does not have to collect everything and mail it all it once.
We only ask that your full name appear on each item you send us. Feel free to add other identifying pieces of information if you think your name is common. People seem to like to put their social security number on supplemental documents and while we'll protect that information and limit access to it, we don't need it on every bit of correspondence (SSN is needed on your application to match it with the financial aid record).