I doubt that exactly. Current market prices result from (low) supply and (high) demand. So if I boost demand in cities by giving money to buyers, what happens then?
Part of it ends up with the sellers through higher prices, the other part with the buyers. It is never 0% or 100%, always something in between. Moreover, only owner-occupiers receive it and not investors, who increasingly also buy apartments in cities, so it tends more towards a 0% take-up effect than a 100% take-up effect. It only flows to families with children, not to investors, singles, couples without children, couples with adult children...
There is no need to argue long that this is more a political issue than real support against the housing shortage. But if you get young families to build in rural areas, then you relieve the housing market in cities and support rural areas from dying out. Certainly only marginal effects, but the direction is basically not wrong.
On the contrary, the goal is exactly that sparsely populated areas continue to shrink in terms of population. From an economic and ecological perspective, it is much more sensible if everything concentrates on urban agglomerations including large commuter belts. Rural exodus is sensible from a spatial ecological perspective. This has long been scientifically established, and the specialist politicians of all parties are probably in agreement. Of course, populist statements can always be made now and then for a few votes about supporting the rural population, but basically the direction is clear.