that不可以省略。没有that就不能用and. 这个句型是一种强调，强调状语 very well。是较为正式的用法。

= He plays basketball， and he plays basketball very well.

《韦氏高阶词典》有and that的这种用法。

and that

1 somewhat formal — used to refer to an idea just mentioned

• He was helpful, and that to an unusual degree. [=he was unusually helpful]