If SHA-256 gets completely broken, then yes. However, such instant breakdown may not happen in practice:
* weaknesses found usually still require some computation time, which may be prohibitively expensive. Reducing 2^128 to something like 2^90 is terrible disaster from crypto perspective (and buyer confidence), but won't open floodgates for fake coins (if faking a coin costs thousands times more than mining/buying, then nobody will bother on large scale).
* attacks typically have certain limitation, e.g. only generate collisions, but not preimage, or apply only to certain types/lenghts of data. Hash could be totally broken for one set of cases (MD5 digital signatures are useless) and at the same time still hold strong for other (MD5-hashed salted passwords are safe, as best known preimage attack is 2^123), so even if some terrible flaw in SHA256 is found, it may not be applicable to the way Bitcoin uses the hash.
* weaknesses found usually still require some computation time, which may be prohibitively expensive. Reducing 2^128 to something like 2^90 is terrible disaster from crypto perspective (and buyer confidence), but won't open floodgates for fake coins (if faking a coin costs thousands times more than mining/buying, then nobody will bother on large scale).
* attacks typically have certain limitation, e.g. only generate collisions, but not preimage, or apply only to certain types/lenghts of data. Hash could be totally broken for one set of cases (MD5 digital signatures are useless) and at the same time still hold strong for other (MD5-hashed salted passwords are safe, as best known preimage attack is 2^123), so even if some terrible flaw in SHA256 is found, it may not be applicable to the way Bitcoin uses the hash.