Given the common ancestry of the Romulans and the Vulcans, and that the Romulans emigrated only about 2,000 years ago (in the TNG era: a drop in the bucket in terms of evolutionary biology), should there be a number of Romulans capable of initiating a mind meld? Is it ever explicitly shown that they can mind meld or that they specifically can't mind meld?
They used to have telepathic abilities, but not anymore. Expanded universe reference on Memory Alpha states:
It is explained in Vulcan's Soul that the Romulans rejected the telepathy of the Vulcans and slaughtered or enslaved the telepathic ones among them during their exodus to the Romulan system: the telepaths became the Remans.
Also the Romulans missed out on the spiritual/social Renaissance that the Vulcans underwent where they tamed their emotions and mastered their minds. Where Vulcans began a process of reflection and mental discipline, the Romulans focused on conquest and empire building. Not only that but, as mentioned by @HNL, they rejected the meditative lifestyle entirely, going out of their way to excise those with telepathic potential from their society.
The Romulans demonstrate some latent telepathic ability in the two-part episode TNG: Gambit where a Romulan uses the Vulcan psionic resonator that "focuses and amplifies telepathic energy" Thus they demonstrably have similar telepathic capabilities to Vulcans.