Now that the following Museum publications have been added to JSTOR ...
Metropolitan Museum of Art Bulletin 1968-2000
Metropolitan Museum Journal 1905-2000
Metropolitan Museum Studies 1928-1936
Recent Acquisitions 1985-1988 (stand-alone issue)
Notable Acquisitions 1965-1985 (stand-alone issue) ...
... it is possible to search for Met objects by accession number, provided of course that the number is included somewhere in the article. You can search by accession number in almost any of the JSTOR search interfaces, though I recommend Advanced and Expert. In the Advanced search, use either the "All of these words" or the "Exact phrase" text entry boxes. Enter the number exactly as you see it, with the periods.
JSTOR is essentially performing a keyword search on the full-text, which includes both words and numeric strings. Unless you specify a specific field to search (e.g. title), a default full-text search will search absolutely everything - articles, footnotes, bibliography, captions. As the accession numbers are often included in captions, they will thus be retrieved.
Try the search below for the Dogon Seated Couple: Accession number: 1977.394.15