Can I use a space in an option name/key?

Other than general WordPress practice (http://make.wordpress.org/core/handbook/coding-standards/php/) which encourages spaces to always be replaced with – in file names and _ for other purposes, there isn’t a set reason that you can’t use spaces in an option name.

From my tests, there is no technical reason to limit you from using a space.

(edit) looking further, the SQL is:
$row = $wpdb->get_row( $wpdb->prepare( “SELECT autoload FROM $wpdb->options WHERE option_name = %s”, $option ) );

so any escaped value should work but just to be safe, you should always use esc_sql() as it doesn’t do it specifically.