The classic Cybermen have been featured several times in the revival.
The Cybermen in "A Good Man Goes to War" lacked the Cybus Cybermen emblem and "monitoring sectors" seems more up their alley than Cybus Cybermen (seeing as how the Cybus versions were notably less advanced than our universe's). The Cybermen featured in "Closing Time" were promoted as being the Mondasian Cybermen.
In "Dalek" the Ninth Doctor and Rose saw a Cyberman head from the classic series era, and the Ninth Doctor told Rose that the Cybermen had been wiped out during the Last Great Time War.
The fact the Cybermen seen in "Nightmare in Silver" and "Closing Time" are not identical to the classic series Cybermen doesn't mean anything, as in the classic series their appearance evolved over time. The Cybermen in "The Tenth Planet" and "The Moonbase" look nothing like the Cybermen in "Silver Nemesis".
Writer Neil Gaiman has said that he believes the Cybermen in his episode "Nightmare in Silver" were made as the result of the Cybus and Mondasian Cybermen uniting into one race. However, as nothing in-universe has confirmed this, any future writer is free to disregard this idea.