A small value of the cosmological constant(vacuum energy) is the simplest source of dark energy, and indicates that we live in a asymptotically de Sitter universe.
This means that our Universe asymptotes to a de Sitter space.
De Sitter space is the maximally symmetric solution of the vacuum Einstein equations with a cosmological constant (curvature).
An observer in a de Sitter space is surrounded by a cosmological horizon. The horizon is observer dependent.
No, the observation of CBR is not proof that we do not live in such a space.
You are correct, our universe is similar to (asymptotically approaches) a de Sitter universe.
Our universe has CMB, and asymptotically approaches a de Sitter space, but that is not necessarily always true the way around. Not all de Sitter spaces would have CMB.