Is a turtle really a turtle without its shell?

Technically yes but it would probably be dead.

A shell is a defence mechanism for the turtle, it protects its body from predators and just general accidents. Although if a turtle is without a shell it wouldn't have its spine or ribs, this is because they are fused with the top of the shell, thus is called a caraoace and it protects the turtles lungs, so if the turtle is without its shell it would be hnically be a turtle but it would a dead turtle because the shell is part of its body and therefore it grows with it.