Nee, het komt van het woord 'geldkist', kas. En nadrukkelijk niet van die Chinese munt. Lees maar:
Cash - 1593, from M.Fr. caisse "money box," from Prov. caissa, It. cassa, from L. capsa "box" (see case), originally the money box, but the secondary sense of the money in it became sole meaning 18c. Verb meaning "to convert to cash" (as a check, etc.) is first attested 1811. Like most financial terms in Eng., ultimately from It. (cf. bankrupt, etc.). Not related to (but influencing the form of) the colonial British cash "Indian monetary system, Chinese coin, etc.," which is from Tamil kasu, Skt. karsha, Sinhalese kasi.