Not that much. Here is some neglected wisdom from David Weisbach:
This simple intuition [about status] does not tell us anything about the likely effects of status on the tax rate schedule. For example, increasing progressivity would move everyone closer together. This might decrease status competition, because the gains from competition are smaller – it would be harder to separate yourself from the group. On the other hand, it might increase status competition. If you are closer to beating someone in a status race, you might try harder. Thus, we can imagine status considerations leading to either a more progressive tax system or a less progressive tax system.
The paper basically combines the substitution effect and the threshold or portfolio effect to argue we should not be too quick to infer particular policy conclusions from considerations of relative status.
Furthermore a consumption tax doesn’t necessarily limit status games through consumption (e.g., buying a bigger yacht), though it may postpone them. A consumption tax encourages savings, which ends up converted into future consumption. The status/consumption game will be all the more intense in the future. The only way to lower the total amount of these status games is to…umm…lower real gdp. Which is not a good idea.