If I disable wp-cron from config, will automatic updates still work?
No, neither will scheduled posts, transient cleanup, trash clearing after 30 days, or automatic plugin updates, and some other things. Anything that relies on timed or scheduled activities will break.
It seems you already know the solution, though the real solution is to identify which cron jobs are using so much CPU and fix those. Changing how cron runs from WP Cron to a crontab will give limited relief.