I am not sure why one would do that.
If a VAT is added on top of the current income tax, what difference would it make? It's simply another tax. The tax defered account maintains its advantages and disadvantages. And, I don't see a difference for not tax advantaged money.
If a VAT is added and the income tax is reduced by the same dollar amount then things get interesting. The tax deffered account starts to look good since, upon withdrawal, one would pay a lower tax rate. Roths may look worse since the taxes on the initial contributions were paid at the earlier, higher rate - but one still has the tax free earnings to offset that. Withdrawals from non-taxed advantaged money would remain the same - no tax since it has already been paid.
If I am wrong or have left something out, please let me know.
Additions to taxable accounts instead of a 401K would make sense if the current tax structure of significantly lower tax rates for Capital Gains and Dividends is maintained indefinitely.
As to VAT, i suspect that I would be much easier to sell politically if it is presented as a replacement for our current income tax. The government would have several incentives for going this way
1) Easier to collect and enforce
2) 401 k, IRA, Roth don't matter anymore Gov still collects tax revenue
3) Probably can be sold to the public as a "fair" tax everybody pays
4) Most people won't have to worry about tax preparation headaches
5) Economic distortions and complexity from current tax system and tax credits and tax exempt entities will diminish.