Hiya Rhonda,
In my opinion pinging websites is useless and in fact can be damaging to your site due to:
1) The amount of spam comments which follow. Its almost 100% guaranteed you will get a wave of spam comments after spam... Plugins like Akismet, Spam destroyer may stop them displaying but you still have to delete them within WP admin. I've had sites which have got tens of thousands of them in a matter of weeks.
2) Worse - you run the risk of having your content stolen! Especially if a site which has more authority metrics steals it, then chances are it will get credit for the content before G's crawlers will have visited your site.
3) You also increase the chances of your website being hit by hacking attempts - access via wp_logon via xmlrpc.php. One of my sites a hacker script has been running continuously for over a year attempting to gain access. Its slowly eating away on server resources with rotating IP proxies (I can still see it in my server logs). I've stopped any chances of it getting access via removal of xmlrpc.php using .htaccess file, but rotating IP proxies still means they visit my site. In addition your website could be exploited as part of DDOS attacks. For example:
Source: [URLnf=http://www.incapsula.com/blog/wordpress-security-alert-pingback-ddos.html]http://www.incapsula.com/blog/wordpress-security-alert-pingback-ddos.html[/URLnf]
For info on pinging and spam:
[URLnf=https://wordpress.org/support/topic/recent-flood-of-spam-via-pingtrackback]https://wordpress.org/support/topic/recent-flood-of-spam-via-pingtrackback[/URLnf]
[URLnf=http://www.wpbeginner.com/beginners-guide/what-why-and-how-tos-of-trackbacks-and-pingbacks-in-wordpress/]http://www.wpbeginner.com/beginners-guide/what-why-and-how-tos-of-trackbacks-and-pingbacks-in-wordpress/[/URLnf]
For info on how to remove access to xmlrpc.php via .htaccess:
[URLnf=https://wordpress.org/support/topic/resolving-xmlrpcphp-ddos-attack-with-htaccess-redirect]https://wordpress.org/support/topic/resolving-xmlrpcphp-ddos-attack-with-htaccess-redirect[/URLnf]
[URLnf=http://perishablepress.com/wordpress-xmlrpc-pingback-vulnerability/]http://perishablepress.com/wordpress-xmlrpc-pingback-vulnerability/[/URLnf]
I hope that helps!
Cheers,
Sid