Yes. While the reorganization of the German states following the destruction of the HRE and the creation of the German confederation (fall of the Kleinstaaterei) existing small european states were still European states (and the Czar's support guaranteed Napoleon got his own small state despite being deposed).

taken seriously?

what does that mean? His son and heir would legally be the ruler of elba; however, how long it would exist in practice is impossible to know given the counterfactual nature of the claim (e.g. how does an unstable french political system react to a Napoleon in power? what changes to prevent the 100 days, etc.).

Also counting against Napoleon while he had a "real" state it was a pretty toothless state. It had a tiny army and the British navy had a loose watch on the island. So the "empire of elba" had no way to force others to take it seriously as a diplomatic player besides the man and the Napoleonic name and legacy. Assuming all else equal (which is probably a horrible thing to do considering it's napoleon and revolutions are on the horizon with or without the 100 days campaign) the long term fate of the Empire of Elba is an existence as a minor european state with no practical power while still being an actual small state.

so tl;dr Yes.