That was intended for people with visual or hearing disabilities. Different apps would speak, vibrate, magnify etc. In order for the apps to be able to be called more easier (say long-press the search button) they would need the user's consent to always be available while in any app. This is the "accessibility" setting.
Other apps have found a way to be useful in using this feature for various means. I believe the reason it says "...the application can collect all the text you type..." is when you are using the feature and you press your button to activate it, it will read aloud what is on your screen. So if you have your credit card info on screen, it may read it out loud.
As for NoLed and Adw Notifier, it won't slow the app down one way or the other. However if it was designed to use the setting and you are not giving it the privilege, then it may not work properly. Try using the app without turning the setting on, if it works then fine.