A polymer is sometimes defined as a macromolecule with MW larger than 1000 g/mol. So can graphene be considered a polymer?
Wow. Good question. Graphene is not considered a polymer in the traditional sense. While it is used a doping agent for other polymers it does not have the designation of being one itself, the allotropes of carbon, at least in my experience and that of my adviser, are typically in a class of their own. Unique structures such as buckminsterfullerene and diamond differ from graphene only by the angles between the carbon atoms, 3-d shape, (and number of carbons present). All of which are definitely not considered polymers. Also remember that a macromolecule is composed of polymers. http://www.macrogroup.org.uk/schools/polymer_chemistry.php
So the short answer would be no, graphene is not considered a polymer.
The common usage of the word "polymer" does not quite match the definition of it as "a macromolecule composed of repeated subunits". Looks like that the definition contains a specification note, tacitly assumed by everybody but never stated explicitly, which says that the subunit in question (i.e., monomer) must exist as a molecule in its own right. That would include all plastics, but exclude covalent crystals like graphene, diamond, silicon, red phosphorus, boron nitride, silicon carbide, quartz, etc.
On the other hand, buckminsterfullerene is a molecule with double bonds, and if we break some of them and connect the molecules together, we obtain a thing which (while still being a carbon allotrope) is rightfully called polymerized fullerene.
I think it boils down to semantics at the end of the day. While it does seem a bit unnatural, I don't really see a problem with saying that graphene is a 2D polymer of repeating "C" units.