Yes — that's a rich and defensible metaphor, though it needs some unpacking to see how far it carries.
Where the metaphor works well
A Hermitian operator (or matrix) has two defining features that map nicely onto scientific practice:
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Real eigenvalues. Hermitian operators are guaranteed real spectra. Science similarly aims at observables that yield real — i.e., intersubjectively stable, measurement-reportable — values, not imaginary ones. The "vocabulary" of science (its terms, quantities, models) is disciplined so that its outputs can be pinned down as actual measurements.
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Self-adjointness / symmetry. H = H†. The operator equals its own adjoint. This suggests a vocabulary that is transparent to its own use — where the way a term acts on states is mirrored by how states act back on it. In practice, this is like the demand that scientific terms be operationalizable in both directions: you can predict from theory and infer back from data. It's a kind of reflective equilibrium built into the formalism.
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Spectral decomposition. Hermitian operators give you a clean basis of eigenstates — a canonical "alphabet." A mature scientific vocabulary is similarly one where phenomena can be decomposed into stable, orthogonal-ish categories (normal modes, quantum numbers, taxa, etc.).
Where the metaphor strains
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Science doesn't converge on a single final vocabulary the way a Hilbert space has a definite operator. Vocabularies get replaced (phlogiston, caloric, ether), and the "space" itself changes.
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Hermitian operators are a subset of all operators; non-Hermitian ones (with complex spectra) describe dissipative, open, or PT-symmetric systems. Science often deals with exactly those — irreversible processes, measurement, decoherence. So "pursuing a Hermitian vocabulary" might be the aspirational ideal, but much of the actual work is non-Hermitian.
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The metaphor treats the community as a single operator when it's really many competing ones; the "self-adjointness" is more like a social achievement (peer review, replication) than a mathematical property.
A sharper version
You might say: the scientific community's regulative ideal is a vocabulary whose terms are self-adjoint with respect to evidence — each term's forward use (prediction) is constrained by its backward use (inference from observation), and whose outputs are real in the sense of being reproducible. That's the Hermitian aspiration. The actual history of science is the story of non-Hermitian vocabularies being slowly symmetrized, or discarded.
So: yes, as a regulative metaphor it's apt and illuminating. As a literal description it overstates the unity and convergence of scientific language.