not really. any deviation between the relative Fiat value is an arbitrage opportunity.
if there IS any deviation immediately a million trades jump in and drive it back to the relative Fiat valuation of the pair.
why? because the UOA is the most attractive asset. free fiat.
minus the friction involved of course. which is why you see temporary variation in difficult to access exchanges/pairs.
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you just described liquid markets
bitcoin is my unit of account
the most liquid markets in the world right now are usd pairs