I think the etymology according to my old Grove suggests the link: (sorry I don't seem to be able to get the Greek letters to remain as Greek)
CEMBALO or CIMBALO (Italian), a dulcimer, an old European name of which, with unimportant phonetic variations, was Cymbal. According to Mr. Carl Engel this ancient instrument is at the present day called cymbaly by the Poles, and cymbalom by the Magyars. The derivation of cembalo is from the Greek Latin cymba), a hollow vessel; and with the Greeks kumbαλα were small cymbals....
These cymbals and bells in the middle ages were regarded as closely allied, and rows of bells of different sizes, tintinnabula or glockenspiel, were also called cymbalo. Virdung (1511) names zymbeln and glocken (cymbals and bells) together. It was most likely the bell-like tone of the wire strings struck by the hammers of the dulcimer that attracted to it the name of cymbal or cembalo. It is explained here, however, not only for the meaning dulcimer, but for the frequent use of the word 'cembalo' by composers who wrote figured basses, and its employment by
them as an abbreviation of clavicembalo. The dulcimer, or cembalo, with keys added, became the clavicembalo. In course of time the first two syllables being, for convenience or from idleness in speaking or writing, dropped, 'cembalo' also was used to designate the keyed instrument, that is, the clavicembalo or harpsichord just as cello in the present day frequently stands for violoncello.