Disclosing Asperger's Syndrome in cover letter for scholarship
I would think not.  While it would, by default, be considered illegal (in the US, at least) to discriminate based on an asperger's diagnosis, putting it in your application makes it valid information for them to make an assessment of your worthiness.  There are extremes to which this cannot be taken, but they are legally allowed to discuss all (legally) provided information, and they will have extra leeway in defending against discrimination suits on data the applicant volunteered.  If you tell them your age in your application, then it is not illegal for them to talk about your age during the hiring process; if you do not provide it, it is illegal.  You are rather explicitly saying "here's a fact about me, so please take it into consideration in determining whether or not to hire/admit me".  The law does not require them to magically bleach their memories of what you have clearly and explicitly given them and pretend the elephant in the room isn't there.

Some applications may have a separate form in which you can disclose "diversity" information such as race and ethnicity.  These are supposed to be kept anonymous and unavailable to the actual hiring committee.  They are just meant as data collection methods to establish they are compliant with laws regulating discrimination and diversity.  If this form asks you about mental health matters, you could certainly feel free to respond to it if you are comfortable with doing so.

I personally wouldn't volunteer any protected information if there wasn't something else in the application that made it sort of obvious, and could be very negative if left unaddressed.  A prolonged period of unemployment may warrant some sort of comment, for example.