yes, all the foot start crank without the key on ... yes, the starter draws a lot, way more than anything else, which is why regular electrical system checks are good
your battery may have been a bit low to begin with, and you may have some less than perfect connections, as well as cables that are lighter gauge than 6V needs
get your battery a load test to see if it can really hold a charge well, and
check that your cables are heavy enough, not the common off-the-shelf ones meant for 12V
Bill