Not exactly. However, as a fan of Sonic and the Black Knight, I've always held the belief that outside of Sonic's genuine desire to do good in the world his mentality of "gotta go fast" is in part a response to knowing that everything he knows will one day come to an end.
I usually have a difficult time getting my thoughts across but here's my take: Sonic is very much aware that he will die one day and everything he's known will also experience a similar fate, yet rather then worry about the future and or try to prevent this he's completely accepted this factoid of his existence and is instead more content with living for the present and not worrying about the future till later. After Sonic successfully prevents Merlina from making the world of Camelot into a eternal world without death Sonic comforts her fears and essentially tells her that, while everything comes to an end and it's quite sad, she should use the time she's given to live life to the fullest and be happy. So ultimately in my perspective and the perspective of others, Sonic's mindset can be considered less of "gotta go fast" and more like "got to do what I got to do, and fast.". Though bare in mind that this is my interpretation of the matter anyway so take it for what you will.