Their application processes are online and in their forms they all ask
if I've signed an NDA or any other document that would limit my
ability to work for them. I answer yes but I also want to attach my
NDA to my application so they can assess that themselves (I don't want
to see my chances cut so bluntly). Is it OK to do that?
The key phrase in the application is "limit [your] ability to work for them".
Most often, signing an NDA with one company would not prohibit your working for another. But the only way to know for sure is to understand the document you signed.
Before signing an NDA, you must read and understand it. If you don't understand it, bring it to someone who can explain it to you, and only then sign it.
Now, you are asking if it's okay to give this prospective employer a copy of the signed NDA and let them determine if it would cause legal troubles for you. This is a very bad idea for several reasons:
- The hiring company is not your lawyer. They are not in the business of advising you of your potential legal troubles. You may need someone who represents your interests, not the potential employer's.
- You will be letting a prospective employer know that you signed a document without understanding it (assuming you actually read it before signing). That says something about your judgement that you may not want to let hiring managers know.
- Asking them to make the determination of the NDA's impact sends them the message that you aren't capable enough of figuring it out on your own. That's not a good message to send a prospective employer - it makes you look less than resourceful.
- It's possible (although unlikely) that the NDA document itself contains information that shouldn't be shared with other companies. Handing it over could violate the terms of the document.
You need to read and understand the actual NDA document now. If you can't, find someone you trust to read it through and explain it to you until you understand it. Then you can determine for yourself if it actually limits your ability to work for others.
If (as I suspect) it doesn't prohibit such work, then in the future, you can answer "No" to this question.