Matt Mitchell says no:
It turns out that in 23 U.S. states, the government will automatically shut down in the event that the governor and the legislature fail to agree on a budget. In his work on budget rules, David Primo examined the theoretical impact of these provisions from a game theoretic perspective. He noted that in states with an automatic shutdown provision, “the legislature will be able to achieve its ideal budget, so long as the governor prefers it to no spending.” (p. 102)
He therefore predicted that states with such a provision will spend more than states without such a rule. He then tested the hypothesis, controlling for a number of other factors known to impact state spending and found that states with an automatic shutdown provision actually spend about $64 more per capita than other states. As he notes, “This effect is remarkably large, given that shutdowns occur rarely.” (p. 103)
This suggests that the federal government’s automatic shutdown provision—by making Congress’s desired spending level a take-it-or-leave-it offer—tends to bias the government toward more spending. By extension, it also suggests that a government shutdown will shift negotiating power toward those who favor more spending. So, paradoxically, fiscally-conservative Tea Partiers stand to lose the most if the federal government shuts down.
Maybe you’re not convinced by that $64 difference. Maybe you ascribe it to unobserved variables. Still, it is hard to argue, based on the evidence, that shutdowns help the cause of fiscal conservatism.