This paper uses a one-dimensional, physics-based model of a valve-regulated lead-acid (VRLA) battery to examine the impact of demand response on uninterruptible power supply (UPS) availability in a datacenter. Datacenters are facilities that provide services such as cloud computing, web search, etc. They are also large electricity consumers. An energy-efficient 15 MW datacenter, for instance, may pay $1 m per month for electricity. Datacenters often utilize VRLA batteries to ensure high reliability in serving their computational demand. This motivates the paper's central question: to what extent does the use of datacenter UPS batteries for demand response affect their availability for their primary purpose (namely, emergency power)? We address this question using a physics-based model of the coupled diffusion-reaction dynamics of VRLA batteries. We discretize this model using finite differences, and simulate it for different datacenter battery pack sizes. The results show that for a typical datacenter power demand profile, a VRLA battery pack sized for UPS functionality can provide demand response with only a minimal loss of UPS availability.