Question about Google Applications

I've connected my google applications to Zoho

I wanted to know, if I send emails from Zoho, does this appear in my sent box in my emails?
And if I get a reply to an email sent from Zoho, does this reply also appear in my Zoho account?

So far, the answer for me is: no!

I thought this was the whole point of integration with Google Applications?

Thanks

Omar