Remember, an appeal is only focused on one specific issue -- the matter that is being appealed. No more, no less.
So, no, appealing by itself does not automatically open up pandora's box and exposes GOOG to laches again.
The risk of an appeal -- again, considering that it would only get this far in the absence of a settlement -- is that VRNG would cross-appeal on laches (i.e. VRNG would specifically file an appeal requesting that laches be revisited).
Also keep in mind that if there is no settlement, that VRNG could appeal laches regardless of whether GOOG appeals or not.
Simply as a matter of strategy, one would expect that -- again, in the absence of a settlement -- both parties would file appeals if for no other reason than to maintain leverage during post-judgment settlement negotiations.