Old English, Middle English, and Modern English all have threads of commonality through them, but how recognizable would the Conquistadore’s Spanish be to a modern Spanish speaker?
I answered a very similar question a few years ago, with specific mention to Hernán Cortés. I hope you find my answers useful:
https://www.reddit.com/r/AskHistorians/comments/7x4dyy/could_a_modern_day_spanish_speaker_have_a/