No. Copilot is a technical preview. In the final release, if it reproduces code verbatim, it'll tell you and present the correct license.
https://docs.github.com/en/github/copilot/research-recitatio...
Are you doing that? If not, then I wouldn't use GitHub's use as justification to engage in copyright infringement.
Will it check the LICENSE file? Simply having a LICENSE file is not a declaration that all the code in that repo is under that LICENSE.
What if specific lines/files are specified to be under different licenses?
What if the publisher of the repo is publishing it under an incorrect license in bad faith?
Will github be responsible if it tells me the wrong license?
No. Copilot is a technical preview. In the final release, if it reproduces code verbatim, it'll tell you and present the correct license.