No, structural asymmetries present in the original images are maintained in
the transformed brain, assuming that they don't dominate the image. For
instance, left and right Heschl's gyrus differ on the rostral-caudal axis
in normal brains and this difference is maintained when transforming the
brain into MNI space because the linear transformation can not alter
relative positions within the image. If the asymmetry was enormous, on the
other hand, then it would be reduced by trying to match a normal
template. For instance, large lateralised strokes and hydrocephalus
typically wreak havoc with registration.
Hope this helps.