I think its a bit more complicated than that - depends on B2B and either B2 'normal' C or B2 'sophisticated' C.
B2B - not a problem, they are used to seeing net prices and in most cases can claim VAT back anyway.
B2 'sophisticated' C (someone who buys a lot online and understands whats going on better) will be fine seeing final price suddenly jump up as VAT added. (though this is against EU law as I understand it as prices to consumers should be shown gross - never mind that its impossible to actually comply)
B2 'normal' C - the prices they see day to day will be gross (VAT inclusive) and they probably dont ever think about whats going on with the tax. (The tin foil hats amongst us will realise that this is probably not an accident, why wouldn't a govt try and hide what its actually taking out of your pocket?).
I've no answers - just pointing out that different types of consumers are likely to see things very very differently.