It does not, or at least it does not significantly impact page load time.
Please read this http://www.dansmart.co.uk/2016/01/wordpress-post-meta-caching/
Large amounts of custom fields may impact page load time a tiny bit because a lot of information is being retrieved and transmitted from the DB, but the amount of data would need to be excessively huge for each post to be measured in more than microseconds.
