One thing we can look at to sort of answer this is Viking settlements in Canada. There, the Vikings - though they weren't necessarily looking for a permanent settlement - were driven out by hostile Native Americans that they just couldn't win against.

Equally, it's also well-worth considering that even with guns, Europeans couldn't just stomp Native Americans. Certainly in Mesoamerica, Cortes was only able to conquer Tenochtitlan because of substantial aid from other local groups like the Tlaxcala. The same is true in South America, where Pizarro conquered the Inca not because of technological superiority - the Spanish got rid of their steel armour, for instance, and their horses were nearly useless - but because of civil unrest in the empire. Indeed, when we look at North America, we see settlements like Jamestown nearly dying several times specifically because they couldn't win against the Native Americans.

Essentially, guns weren't the be-all, end-all of why colonisation of the Americas succeeded.

Sorry, but your submission has been removed because we don't allow hypothetical questions. If possible, please feel free to rephrase the question so that it does not call for such speculation, and resubmit Otherwise, this sort of thing is better suited for /r/HistoryWhatIf.

This is a speculative question and thus by it's nature hard to answer, but I can give you my opinion.

If you look at the early records, when the Spaniards for the first time landed at the coasts, it is often reported how a single shot in the air led the entire indiginous population to lie on the floor in terror.

I would therefore say that powder weapons were critical for the victory of the Spaniards, but they played a far greater role in their psychological effect rather than their actual use in battle.

But of course, the Conquistadores were often outnumbered and their victories were achieved mainly due to their superior technology and training. One example amongst many is the Battle of Otumba.