It really depends what you mean by "scattering state".
On the physical side, Bloch electrons are still bound in the sense that when you have a lump of metal in vacuum, the electrons will not spontaneously boil off - they remain confined to the crystal. This subtlety is not really easy to see in the typical Bloch formalism, which is derived for a torus-shaped crystal.
Likewise, a conducting wire's electrons remain confined to the wire, suggesting that conduction band electrons also reside (well) below the vacuum energy of an isolated electron.
Imagine you take the material and remove all of its itinterant (movable) electrons, so you just have bare ions. This electron is described by the Hamiltonian $H = \frac{p^2}{2m} + V(r)$, where $V(r)$ is periodic. The Bloch argument makes sense for these electrons' periodicity then goes through. Note that, like the Hydrogen atom, there are in general infinitely many bound states $n=1,2,3,4,...\infty$ that converge to a continuum above $E=E_{vacuum}$.
The standard narrative goes that because electrons are Fermions, you can only have two in every state and gradually "fill up" the available slots in the spectrum. This system is called a Fermi gas - you have $N$ Fermions that do not interact except in the sense that they aren't allowed to double occupy a state.
This is only part of the story - if it were true, it should be possible to have a bound $H^{10-}$ ion, but any chemist would immediately throw you out of the building for even suggesting it.
When analysing the spectrum of a single electron Hamiltonian, you will generically find two classes of states - those with discrete eigenvalues and those with continuous eigenvalues. In a hydrogen atom these correspond to bound and scattering states, with the former corresponding neatly to electrons below the vacuum energy.
This immediately gets cooked when you add more electrons - $H^{-}$ has a (weakly) bound state, but it no longer makes sense to discuss what a single electron does because it is influenced by the repulsion of the others. It turns out that in most materials (so-called "weakly correlated" materials) this doesn't change very much about the system except for pushing the energy up a bit, so that there is a point where the repulsion of the electrons overcomes the nuclear attraction. This is called a Fermi liquid, i.e. a Fermi gas where the energy levels change slightly depending on how many electrons are in the system. Generically, this means that there's some number of electrons at which you run out of space for bound states.
The point of all this? You have a system with, say $N$ monovalent atoms (e.g. Na$^+$) and $N$ electrons. They can't all sit in the lowest available energy state because they're Fermions, so they have to fill up the "slots" in the spectrum. There's usually room for many more electrons than are present in a neutral material, so there's a final energy $E_F$ where you run out of electrons. This is the Fermi energy.
The bands (i.e. $k$-labeled energy eigenvalues) that lie below $E_F$ are "valence" bands, those that lie above are "conduction", but the nomenclature is terrible because both kinds of bands can be involved in conduction of electricity. (Crucuilly, $E_F$ is generally far below the energy of the closest unbound state. The energy required to "ionise an electron" (read: remove an electron at the Fermi level to the vacuum energy) has a name, called the work function $\Phi$.)
On the other hand, you can pull a pro gamer move and redefine the Fermi energy to be the vacuum energy. Now, there are two kinds of elementary excitations: an electron in a conduction band (call this $e^-$) and a missing electron in a valence band (call this $h^+$). Their wavefunctions are essentially still Bloch wavefunctions, and both have positive energy, so in a weird sense, you can view these both as scattering states. On a macroscopic level though, they wont leave the material - there's still the extremely strong confining potential of the nuclei keeping them around.
