tl;dr:
R&D spending cannot stimulate economy during just by increasing long-run aggregate supply because recessions are fluctuations around the long-run aggregate supply and not necessary affected by the long-run aggregate supply.
A in which spending on R&D in principle could be more effective in fighting recessions than other spending. The effectiveness of spending on increasing output through the multiplier depends on marginal propensity to consume. Hence, a redistribution of resources from people with low marginal propensity to consume to people with high marginal propensity to consume is helpful in increasing the effect government spending has on the economy. If you could argue that people who work in R&D have higher marginal propensity to consume than other people you could argue spending on R&D is more effective. However, I would be extremely surprised if this would be the case, because it is established that marginal propensity to consume decreases with people's incomes and people engaged in R&D tend to be one of the better payed workers (see For example above mentioned Blanchard et al).
Full Answer:
Not in general, even though spending on R&D might be beneficial for long run growth, it is not, in general, any more effective in stimulating economy in recessions or more effective response than some other spending. There are several reasons for this.
First, a recession (especially demand driven one) is, from a perspective of macroeconomics, a short-run phenomenon. As opposed to microeconomics in macroeconomics long run has slightly more vague definition but scholars generally agree on that it is a very long time period.
For example, Blanchard et. al. in Macroeconomics a modern perspective offer probably most vague definition of long-run:
long run A period of time extending over decades.
More advanced texts such as Romer's Advanced Macroeconomics use the term long-run to define a period in which all relevant variables (wages, prices etc.) adjust to the state of the economy.
Depending on the book/research paper the definition might slightly vary but these definitions imply that in general recession is a short-run phenomenon, not a long-run one and this hold especially true for demand driven recession.
To clarify, recessions is defined as defined as a period of negative growth of economic output (and for statistical/research purposes often as negative growth of output for at least two consecutive quarters - again see the above cited Blanchard et al.).
Under either of the above definitions of long-run recession would generally not qualify as a long run phenomenon. I cant think of any historical example of recession spanning decades, and even if there were such example it would be an exception rather than the rule. Under the second more narrow definition recession could only occur in long-run if the economy's own long-run growth path would itself be negative which is very implausible.
Moreover, under both Real Business Cycle theory and New Keynesian theory of business cycles recessions are considered transitory phenomena. In both of these it does not really matter what is the long-run aggregate supply for the recession - in fact the business cycle occurs as economic output fluctuates along the long-run aggregate supply (See Romer's Advanced Macroeconomcis for more detailed treatment of business cycle theories).
Consequently, the long-run changes in aggregate supply do not affect recessions. Of course, it is desirable to increase the long-run AS as higher output will lead to higher material welfare but there is no reason why increasing economy's productive capacity should have any effect on reducing the size of fluctuations themselves.
In addition, the idea that spending on R&D even affects rate of economic growth and hence the rate at wich long-run aggregate supply expands is somewhat contentious one. In a standard Solow-Swan growth model a economy will growth at an exogenously given rate no matter what is it's R&D spending as technological progress in such models is completely exogenous. In an endogenous growth theories (e.g. Romer model) spending on R&D actually increases long-run economic growth (and thus also rate at which long-run aggregate supply expands). Unfortunately, an empirical evidence is not yet settled on this issue and Solow model is the more accepted one (again see Romer's aforementioned book).
However, there is a way in which spending on R&D in principle could be more effective in fighting recessions than other spending. The effectiveness of spending on increasing output through the multiplier depends on marginal propensity to consume. Hence, a redistribution of resources from people with low marginal propensity to consume to people with high marginal propensity to consume is helpful in increasing the effect government spending has on the economy. If you could argue that people who work in R&D have higher marginal propensity to consume than other people you could argue spending on R&D is more effective. However, I would be extremely surprised if this would be the case, because it is established that marginal propensity to consume decreases with people's incomes and people engaged in R&D tend to be one of the better payed workers (see For example above mentioned Blanchard et al).
Thus to sum up, generally you cant claim that R&D spending is more effective in stimulating the economy and aggregate demand in the short-run than lets say social or infrastructure spending. It also does not make sense to talk about 'long-run solutions' to recessions as they are by definition short-run phenomena (where I take the solution to mean response to a recession and not a policies that might try to lets say reduce likelihood of recession occurring in the first place).
