This is probably a little late, and you might not need the information anymore. But, I thought I'd provide it anyways, as it may help someone else.
Both pregabalin and baclofen are GABA analogues, as well as, gabapentinoids.
A GABA analogue or GABA-mimetic is a drug that is a structural derivative of GABA. Because GABA cannot cross the blood-brain barrier (BBB), they developed drugs that are chemically similar to GABA that do cross into the brain. However, these drugs do not act similarly to GABA, and in fact have a very different primary mechanism of action.
Gabapentinoids (gabapentin, phenibut, pregabalin, and baclofen) are drugs that bind to and inhibit the α2δ-1&2 (alpha-2-delta) subunits of VGCCs (voltage-gated calcium channels). Pregabalin binds to and inhibits these receptor subunits in the DRG (dorsal root ganglion) of the spinal cord, and areas of the brain (PAG, ACC) that process nociception and emotional aspects of pain. This inhibition decreases intracellular Ca2+ (calcium) currents, decreasing the release of excititory neurotransmitters/neuromodulators like glutamate, norepinephrine, serotonin, and Substance P. This causes less pain signals to be transmitted to the brain, decreases neuron sensitization, and leads to a decrease in new dysfunctional neuron synapses that carry pain signals (glutamatergic synaptogenesis).
Pregabalin and other gabapentinoids (except baclofen) do not bind to or modulate GABA receptors, they don't affect GABA uptake or breakdown, but they do increase the expression of L-glutamic acid decarboxylase (GAD), which catalyzes the conversion of glutamate to GABA. So, they can possibly increase GABA concentrations in the brain.
Baclofen is an agonist of the GABA-B receptor (it also inhibits α2δ VGCC subunits, but with 100-fold less potency than pregabalin).
In short: pregabalin is not a GABAergic medication, but baclofen is. Pregabalin may increase overall GABA concentrations within the CNS, but it doesn't affect GABA receptors like benzodiazapines, barbiturates, or baclofen.
And baclofen affects the GABAergic system differently than benzodiazapines, ethanol (alcohol), and barbiturates, which are PAMs (positive allosteric modulators) of the BZD/alloateric (benzodiazapine) site of GABA-A receptors. Therefore, the central and peripheral effects are different, despite some overlap (anxyolysis, sedation, muscle relaxation).
I have taken gabapentin for 14 years, at a relatively high dose, and I have taken baclofen on and off for 3 years with no negative effects that were the result of the drugs being taken concomitantly. However, I do want to emphasize the importance of a very slow titration when decreasing and discontinuing either drug. I have studied gabapentin and pregabalin for 7 years now, run support groups for people suffering from side effects or discontinuation syndromes from pregabalin and gabapentin, and personally counseled people struggling with discontinuing pregabalin and gabapentin and helping them create a safe titration plan. If I did not have to take gabapentin (only thing that somewhat controls my epilepsy), I would get off in a heartbeat. I don't want to sound paternalistic, you have the right to partake in any substance any way you want to. I just want to let you know that some people have vicious withdrawals from gabapentin and pregabalin (and phenibut).
As far as my professional experience with baclofen goes, I have not seen anything too terrible. It is generally well tolerated, and presents very few side effects. And of the people I have helped who had trouble discontinuing it, most were attempting to stop using other GABAergic substances at the same time. It definitely beats chronic alcohol use.