Can a Tensor with NoneTape have gradients recorded? YES

NoneTape just means that the tensor currently doesn't own the tape - but it may gain access to the tape at a later point.

In fact some of the binary operations (e.g. add) expect one of the operands to have a NoneTape.

You can also add the tape to a tensor using .put_tape(tape), and remove the tape from a tensor with .split_tape()