In our opinion the answer is unequivocally no
We would not envisage a situation where search engines would ever look, even less consider it a ranking factor.
For human website users though, it may appear that a site is not kept ‘up-to-date’ if content such as this is not as current as it could be. In reality this is likely to be a minority but in an age where users’ minds are very quickly made up we would say it would be prudent to keep details such as these updated.
From a housekeeping and quality point of view we would recommend keeping copyright dates current.