Only if they no longer buy soft drinks, which means they don’t pay the tax, which means it doesn’t raise revenue.

You seem to be assuming a binary choice in consumption, but the modelling in the study was that those numbers for dental outcomes would be produced by a 24% reduction in consumption of sugar sweetened beverages.

From the SBS article:

Assuming a 20 per cent tax is passed on in full to consumers, the study predicted the price increase would result in a 24 per cent reduction in consumption.

So there would still be tax revenue from the remaining 76% of consumption. But it’s a public health measure, just via a tax, so if it produced no revenue that would (from a public health perspective) be considered a huge success. It makes sense that the amount of revenue you raise and can spend on dental health would scale in proportion to the amount of consumption and dental harm. It’s a way of partially de-externalising the health externalities of the sugar-sweetened beverage industry.

It’s of limited imparting also note that (1 + 0.2) x (1 - 0.24) = 0.912. So with a 20% tax, modelled to reduce consumption by 24%, on average people will be spending 9% less on sugar-sweetend drinks.

Or they keep buying soft drinks, pay the tax, and end up even poorer which will increase the likelihood of further health issues.

As pointed out by @observes_depths@aussie.zone, if the revenue is directly tied to funding dental care for poorer citizens, care which someone who maintains 100% of their consumption is more likely to need, then they may end up less poor than otherwise. Not only is their tax contribution going into that funding, but revenue from wealthier consumers and those who have reduced their consumption and are less likely to need dental care.

I’ve also seen proposals where the money is spent on subsidising fresh food, so that the average weekly shop comes out to the same dollar figure even if behaviour doesn’t change, while people are doubly incentivised to make healthier choices.

The SBS article also mentions that the tax can be designed to encourage reformulation of drinks, with drinks below a certain sugar concentration exempted from the tax, as happened in the UK:

In 2018, the United Kingdom introduced a tax of 19.4 or 25.9 pence per litre, depending on the sugar content of beverages.*

It led to a 46 per cent reduction in the sugar contained in soft drinks, the UK government said, with nearly 90 per cent of the market now containing sugar below the level at which the tax applies.*

So in the UK 90% of drinks are no more expensive to the consumer, but tax-incentivised reformulation has meant sugar consumption from sweetened beverages has decreased by nearly half! (Again, revenue raising is not the aim, the tax is just a policy ‘stick’.)

The study the SBS article is about also modelled for a similar level of reformulation:

The health impact of the SSB tax is up to three times larger with 50% reformulation as compared with the base case and nearly five times with 100% reformulation.

A 300% greater health impact over the ‘base case’ (20% tax, 100% passed-on), and it’s hip-pocket neutral 90% of the time!

Your arguments can equally be applied to the tax on tobacco, but we know that applying a tax (to a point, it seems!) reduces tobacco consumption and the associated health harms, and provides revenue that makes up for the cost of tobacco-related disease to our health system.

A sugary beverages tax like the ‘base case’ (20% tax, 100% passed-on) would be similar to the tobacco tax and could be used to similar effects, but, as I hope I’ve made clear above, there’s lots of options.

Ok, but now there’s all this extra money from the sugar tax and even more from heath care savings, and that can be used to make a meaningful difference helping the poor.