Yes (and possible no). When you draft an e-mail there should be a small "check box" (white square looking) at the top (above your "From" line) next to the phrase "return receipt" ... that is what you check to get the requested receipt.
And the no ... when I ran a Help Desk, we disabled the return receipt. Why? So that the users did not see when we opened and catorgized their request. This is necessary to triage work, and keeps the user from hounding us with "but you read my email..."
Send a message to yourself with the read receipt and see. Let me know if it works for you...
The issue may be incompatibily with other email systems. If you send to another verizon account does it work?
As stated above the user could also have that feature tunred off, as I do, but I use Zohomail to view my VZ account.