Is this sydnone aromatic?
As correctly pointed out in the comments, the compound you present belongs to the class of sydnones. According to Hückel's rule, it should be aromatic, as the molecule is planar and contains $4n+2$ π-electrons.

However, calculations performed in 1998[1] that mainly looked at chemical shifts and inferred aromaticity from the magnitude of observed diamagnetic shielding, show that sydnones in fact are not fully delocalized, i.e. they are not aromatic. To quote from the linked publication:


  Mesoionic compounds  are  planar  five-membered  heterocyclic  betaines
  with at least one side chain whose α-atom is also in the ring plane and with dipole moments of the order of 5 D. Electrons are delocalized over two regions separated by what are essentially single bonds. One region, which includes the α-atom of the side chain, is associated with the HOMO and negative π-charge whereas the other is associated with the LUMO and positive π-charge.


The publication is also riddled with images that depict syndones like this:



It ends with another quote from Gilchrist's book "Heterocyclic Chemistry", 2nd edition, 1992, p. 329:


  It does not therefore seem useful or appropriate to classify sydnones and other mesoionic compounds as aromatic, despite the existence of a cyclic array of p-orbitals.


Reference


Simas, A. M.; Miller, J.; de Athayade Filho, P. F. Are mesoionic compounds aromatic? Can. J. Chem. 1998, 76 (6), 869–872. DOI: 10.1139/v98-065.