Could a carbon tax be a substitute for VAT?

No, taxing externalities is not a good substitute for VAT for several reasons.

1. Pigovian taxes (taxes on externalities) have to be set up in an optimal way to actually reduce externalities. However, it is astronomically improbable that the same level of tax that mitigates the negative externality is exactly the same level that government has to raise for optimal provision of public goods.

2. It can be shown that Pigovian taxes can be imposed without deadweight loss on economy (which almost all taxes have) but such result hinges on a fact that they are made revenue neutral - hence to use Pigovian taxes in most efficient manner you should used them in a way that does not raise any additional revenue.

3. By discouraging the activity that creates negative externality the tax basically by substitution effect erodes its own tax base. Every tax does this to some extent - VAT for example encourage substitution of savings for consumption or substitution away from market goods to non market goods but since VAT is very broad this should reduce tax base much less than just selective tax on goods that create negative externality.

Consequently, Pigovian taxes are ill suited for raising government revenue. Government should still pursue Pigovian taxes everywhere where there are externalities as correcting the externality is always optimal from social perspective. However, no modern government can realistically raise the kind of money it needs to run itself without VAT - in fact it is no accident that modern governments expanded precisely when modern VAT and income taxes were developed, if you check most government budgets VAT and income tax are always the biggest sections on revenue side of budget.

There are some similarities between a carbon tax and a VAT. There is a recent paper on NiskanenCenter.org that compares them in terms of their administrative costs and other features.

If you are looking just for revenue (not for the effect on climate change) one disadvantage of a carbon tax is that its revenue would gradually disappear over time as carbon emissions fall toward zero. If you used carbon tax revenue for, say, rebates to low-income households, you would then face political pressure to introduce some other form of payment such as a UBI financed by general revenue (or, for that matter, by a VAT).