You still haven't answered the main questions, Codae. How would they survive
cut off from Europe? and how would colonists who'd arrive later, react?
1) They wouldn't, not in the long term. A decent example is what happened to the Norse colonization attempts, as is the early English efforts in Virginia. This would be even worse as these wouldn't be colonists, but shipwreck victims. They would have neither crops seeds or supplies and they would be ill prepared to even provide for self defense against a substantial local force (the tech gap is so small that it may as well not exist). There would be no hope of resupply or other help from Europe. Game over.
2) Potentially, given the pestholes that Crusader vessels were, the colonists find a fully populated Hemisphere, not one that has been wiped out by recent plauges, as the population would have time to reconstitute. That presents huge troubles in establishing any serious colonization prior to 1700, perhaps as late as 1800, given the far great opposition by current residents. The technology gap wouldn't be sufficient to overcome that for several centuries.
The problem is where the Crusader ship would come from. Very few crusaders went by ship prior to getting to the Med, even then the preferred path was overland. Ship tech wasn't up to long seaborne voyages. You also have the difficulty of supply, as those few Crusader vessels that did travel did it within sight of the shore.