Does protein kinase A accelerate glycolysis or slow it down?
There is a fallacy in your argument, which is the parenthetical statement:


  so that when energy level is low, the increase in cAMP will cause protein kinase A to increase in activity


The activity of adenyl cyclase (the enzyme catalysing the production oc cAMP) is not controlled by energy charge, but by hormones such as glucagon. That is how glucagon has its effect on protein kinase A (better thought of as cyclic AMP-dependent protein kinase to remind you of this fact). That is why cAMP is known as a ‘second messenger’ — the hormone being ‘first messenger’ (and the enzyme that becomes phosphorylated being the recipient of the message). See, for example, Figure 21.14 from Berg et al.

Therefore the explanation in the Wikipedia article on PFK2 is quite self-consistent:


  When glucose level is low, glucagon is released into the bloodstream, triggering a cAMP signal cascade. In the liver Protein kinase A inactivates the PFK-2 domain of the bifunctional enzyme via phosphorylation, however this does not occur in skeletal muscle. The F-2,6-BPase domain is then activated which lowers fructose 2,6-bisphosphate (F-2,6-BP) levels. Because F-2,6-BP normally stimulates phosphofructokinase-1(PFK1), the decrease in its concentration leads to the inhibition of glycolysis and the stimulation of gluconeogenesis.[8]


So the answer to the question posed in your title is: in liver cAMP causes the inhibition of glycolysis.