No, but it does have something to do with "rupture," as in "break"... "from Italian banca rotta, broken counter (from the practice of breaking the counters of bankrupt bankers) --rotta 'broken, defeated, interrupted'" (dictionary.com)

It is from the Italian "banco rotto"= broken bench. (The past tense of the Latin form of the verb rompere is rupt, which is where English gets its form of the word from). It is, as you assumed, related to the word "rupture" which means torn or broken. The term turned up in the 16th century in Italy, it seems, but there are alternative histories. Wikpedia shows that the lenders of the Renaissance did their business on benches. If they went broke, they broke the bench they dealt on as a sign. Here is exactly what Wikipedia says: "The word bankruptcy is formed from the ancient Latin bancus (a bench or table), and ruptus (broken). A "bank" originally referred to a bench, which the first bankers had in the public places, in markets, fairs, etc. on which they tolled their money, wrote their bills of exchange, etc. Hence, when a banker failed, he broke his bank, to advertise to the public that the person to whom the bank belonged was no longer in a condition to continue his business. As this practice was very frequent in Italy, it is said the term bankrupt is derived from the Italian banco rotto, broken bench (see e.g. Ponte Vecchio). Others choose rather to deduce the word from the French banque, "table", and route, "vestigium, trace", by metaphor from the sign left in the ground, of a table once fastened to it and now gone. On this principle they trace the origin of bankrupts from the ancient Roman mensarii or argentarii, who had their tabernae or mensae in certain public places; and who, when they fled, or made off with the money that had been entrusted to them, left only the sign or shadow of their former station behind them." Our present word bank comes from the word for bench.