General question on smtp

I've recently joined the Zoho mail users, this to avoid problems (blacklisting, not caused by the users of my domain) with my web host.

Did I understand it well that If a mail is sent via Zoho with an smtp of the domain provider that this problem will be avoided?
or do you advice to use the zoho smtp?

if I use Zoho smtp a mail verification is needed, but I don't recieve the verification mail...

Thanks in advance

Thomas