Really old topic, but it wasn't thoroughly answered either. Might as well
One can whiffle about the definition of a brain, but putting things in a realistic perspective, the blunt answer's no. No neurons, no neural activity, no center of any kind for signal processing. (Singular exception to the first two, venus fly traps and similar specimens have a crude synaptic stimuli>response system, but they still don't manage the third).
Edited: daishain on 8th Jul, 2017 - 1:24am
What I want to know… how do collective cells work together to make the final product if there isn't some kind of centralized command? I mean can you imagine working in a factory where everyone has their own job to do but there isn't a supervisor to tell them if they're doing it right or not?