Well yes but compared to what? Any query on the DB is going to add server load and thus page load so your question is not very useful without context.
The PHP code WP uses to order posts randomly is found in query.php:
case 'rand': $orderby = 'RAND()';
Which results in the output like:
SELECT SQL_CALC_FOUND_ROWS wp_posts.ID FROM wp_posts WHERE 1=1 AND
wp_posts.post_type="post" AND (wp_posts.post_status="publish" OR
wp_posts.post_status="private") ORDER BY RAND() DESC LIMIT 0, 10
For example maybe it is 3ms, then obviously using 8 separate DB query’s would add up to 24ms.
Is ordering by RAND slower than a default query or any other orderby parameters, as far as I can tell, no. It is faster than some query params, well..yes.
The actual query speed depends on your server, opcode caching, requests, and all sorts of “things”.