Yes and no. In theory, yes, but, in practice it appears to be no.
In practice, and this is probably more to do with budgets for props than the writers thinking of the actual science (#), the off-world gates and DHDs still seem to be highly similar to the Earth ones, with only a very small handful of non-Earth-gate constellations visible. Also, from every planet we have seen Earth dialled from, the co-ordinates are the same.
In terms of canon explanation, we can suggest that a "standard" symbol is used throughout the gate network to represent the constellations used for "navigation". This removes the need for gate-travellers to re-calculate each address by determining which symbols represent what constellations depending on the planet they are on. These standard symbols happen to be shown by the visual representation from 20th century Earth - spooky huh? They won't represent Earth dozens of millenia ago, nor from most of the planets in the network today (or ever!).
A production over-sight, really.... or shows we have now reached the "right time", and is a highly complex, frighteningly long-planned and as-yet un-revealed plot that will presumably be revealed soon, and probably to the people of Earth by the Ancients. Or is this the plot for the Atlantis spin-off?
(#) There is a separate issue over what is a constellation. I would think it likely that some/many/most of what we consider homogenous constellations are spread so far apart along our line of sight that from "sideways on" they are totally separate, or form several new "constellations" in their own right..... The chevrons would therefore more likely be marking specific locations, perhaps near notable stars, rather than a "constellation" since, as your post highlights, the view changes everything.
