No, the asymmetric unit is the unit that has no crystallographic symmetry in itself. When applying the space group symmetry operations to the asymmetric unit you will get the entire unit cell and hence the entire crystal.
The dimer you see is given by non-crystallographic symmetry (NCS)
I agree with Stefan about asymmetric unit. There is no symmetry elements bewteen 2 independent molecules in the asymmetric unit by definition (I think it is not really correct to call it dimer).
But if you see some possible relation as a mirror plane, rotation axis or inversion between them it is worth countercheck if the symmetry is correct. Try PLATON or CIF Check for additional symmetry check. The best would be to analyse the experimental data again to make sure your model is correct. On the other hand, it is quite usual to have more than one crystallographically unique molecule in the asym. unit.
I was using the CCDC program "Mercury" to look at the unit cell of the sodium sulfate crystal, from 1011184.cif, ZEKGAX.cif, Zeigler et al.. Mercury had transformed the asymmetric unit into the unit cell. There were several sodium ions seemed to be mis-sited as they were much too close to other sodiums.
It would be nice to be able to look at the code that does this asymmetric unit to unit cell operation to see how it uses the symmetry ops and so generates these "oddly placed" sodium ions.