If the application specifically requests you attach a resume in addition (it does not specify it is optional), I would definitely attach it. Even if it is optional, I would still attach it.
Here is a list of reasons the duplicate information in the resume could still be useful.
Providing a resume will allow you to:
- Format your resume to best represent yourself
- Allow you to proofread and weed out careless mistakes
- Provide a buffer against HR departments who don't have their ducks in a line
- Provide a vehicle for a cover letter to further sell yourself for the job
While the system may record all your information, you have no control over how that information will be formatted for viewing by the hiring manager and/or interviewers who will look at it.
Providing a resume as an attachment means that you can format it as you like in a way that better highlights your skills and what makes you good for the job (allowing you to lead the interview in a way that works better for you in the long run).
Make Sure the Info Matches
If you are going to provide both the resume and the application, you will be extra conscious to make sure the information in each matches. And that's a generally good thing to be careful about. Preventing careless mistakes will always work out in your favor.
Who is the Application For?
For all you know, the application could simply be to automate the process of weeding out candidates, and not actually for the purpose of providing info to the interviewers, etc. So HR could just use the "education" field to weed out people without the proper degree, or to limit people with less than X years of experience from moving to the next stage.
Most of us have worked in a company where what should happen (proper sharing of information to all related parties in an ideal format) doesn't actually happen, so providing the resume in addition may prevent some of these problems before they happen.
If the application has no space for a cover letter, by all means attach one! The cover letter is a great way to show that you aren't just filling out oodles of online applications and haven't actually given thought to why you want to work for that company. It also makes you think about how best to fit your experience to what the company is looking for.