Yes, charitable deduction carryovers are allowed when the taxpayer itemizes in the year of the contribution. A carryover is also allowed when the the customer did not itemize, and instead used the Standard Deduction.
I don't see anywhere where you lose your contribution carryover if you used the Standard Deduction in an intervening year, only that you need to adjust your carryover for what you would have claimed in the year had you itemized. The link that @SteamTrain provided says "Charitable contributions (current & carryovers) are calculated for the current year regardless if the standard deduction is used or Sch A is used . The amount that will carryover to the following year is going to be the same with a Sch A or the standard deduction."
The second sentence, "If the customer takes the standard deduction they are losing current year and carryover contributions they may have been allowed had they chosen to itemize." seems to be simply referring to the fact that if you didn't itemize, you didn't deduct that contribution or carryover in that year, not that you lose the opportunity to carry that contribution to a subsequent year.
IRS Publication 526 refers to this situation, but on page 19 states "Special rules exist for computing carryovers if you: • Are married in some years but not others, • Have different spouses in different years, • Change from a separate return to a joint return in a later year, • Change from a joint return to a separate return in a later year, • Have a net operating loss, • Claim the standard deduction in a carryover year, or • Become a surviving spouse. Because of their complexity and the limited number of taxpayers to whom these additional rules apply, they aren't discussed in this publication. If you need to figure a carryover and you are in one of these situations, you may want to consult with a tax practitioner."
Example 2 in this link from Cornell Law School Legal Information Institute shows a calculation where the carryover to a year when the taxpayer chose the Standard Deduction is applied to recalculate the carryover to the following year when the taxpayer itemizes. It's not a perfect example for us, because the carryover gets used up in the year of the Standard Deduction is chosen, but it does demonstrate the principle involved. And this link from Thomson Reuters explains how this works under Five-Year Contribution Carryover.
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