Short answer, CRM is not normally directly related to the Paperless Office settings in Sage 100.
CRM Company information is related to the Sage 100 Accounts Receivable Customer that is linked and a CRM Person would be linked to an AR Customer Contact.

However, changes to an email address in CRM linked to a AR Customer or Contact in Sage 100 would cause that email information to change/update (and vice-versa) via the integration.

What exact version of Sage 100 and Sage CRM are you using?

Which email is changing in Sage 100 Paperless Office:
On that AR Customer's Paperless Office Delivery Options, which value is not correct:

Is it the Sage 100 Customer's email address changing from CRM and the Paperless Office Delivery Options for the AR Customer are set to "Use Customer E-mail Address"?

Or is it the "To Customer Contacts section where the Contact Code and Contact E-mail address are shown?
(If the CRM Person email address is changed for a related AR Contact then this email address can change)

Or is it really the Additional E-mail Address under the "To Additional E-mail Addresses" section of the AR Customer - Paperless Office Delivery Options for the Customer and Document combination?
I can not think of any way the additional Email addresses can be related to a CRM email address for a change to occur in Sage 100.

I sent screen shots of the "before" and after of both sage 100 & crm. We are on sage 100 & crm 2015. It does not appear to affect paperless UNLESS the box is checked to use the customer email address (which most are). IF the main email gets wiped out, the paperless will be blank also

When a contact was deleted in CRM, the contact was deleted in sage BUT so was the main telephone, fax & email address on the customer main page. Why? We have an email blast that needs to go out & we are concerned about making changes in CRM
thanks for the help

- Delete Person in CRM -
You cannot normally Delete a Contact or Person in CRM that is linked to a Sage 100 AR Customer Contact.
The Delete button would be hidden by the integration unless the scripts are not properly running.
If the person is linked to Sage 100 and the button does appear in CRM, it would not delete the contact in Sage 100 but would flag "deleted" in CRM and not affect the Sage 100 AR Customer Contact.
If the Delete button is available on a CRM Person this normally means they are not linked to a Sage 100 AR Customer Contact - even though the CRM Company the Person belongs to is linked to a Sage 100 Accounts Receivable Customer. No changes to this Person would affect Sage 100 as they are not linked.

-Clearing out Email for CRM Person-
Erasing or clearing out the email address for a Person or Contact in Sage CRM should not affect the main email address in the CRM Company and thus not the Sage 100 AR Customer information.

In your case, if you change the email or phone for a Person in CRM, does it update the main CRM Company phone or email?

- Updating CRM Person information -
In normal circumstances, updating the CRM Person related to a Sage 100 AR Customer Primary Contact will update that Contact information but not the main customer information.
Only updating the CRM Company Email will normally update the related Sage 100 Accounts Receivable Customer email.
There are options in Sage 100 CRM Server Options (Customer Relationship Management, Main, CRM Server Options) to prevent changes to CRM Person(s) from updating the Sage 100 AR Customer Contacts:
Uncheck the options for Allow Changes in Sage CRM to Update - "Customer Contacts Related to Primary People" And/Or "Customer Contacts Related to Other People".

If you have not already called into the Sage 100 Support team at 1-800-854-3415 regarding your CRM Integration, I would recommend you do that so someone can see what is happening and when in detail, plus check the settings and configuration.