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Base sizes are critical to the balance inherent in the game - if you start radically changing them it can give a real advantage (or disadvantage) to one player.
Broadly speaking though: bigger = worse. It's a common gripe of people who want to field huge GW dragon models that they suffer from a competitiveness perspective.
All of the above said, I can't think of anyone I've played casually who would strongly object to (much less refuse to play) some slightly bigger unit bases, especially if they're just a bit deeper.
In most circumstances a bit of extra depth on some units is unlikely to affect a game's outcome - and if it did, it's more likely to be to your detriment.
Tournament play is a different matter, and I suspect most TOs will take a firm line on unit footprint.
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