A billion times no to you, sir; exactly the opposite of what you state is true.
Caffeine prevents the anti-hyperalgesic action of gabapentin.
The activity of gabapentin to reduce hypersensitivity to pain is prevented by caffeine.
Caffeine antagonizes the effects of gabapentin.
This study was designed to determine whether 3 weeks of gabapentin treatment is effective in alleviating neuropathic pain-like behavior in animal models of complex regional pain syndrome type-I and partial sciatic nerve ligation (PSNL). We investigated the contribution of adenosine subtypes to...
pubmed.ncbi.nlm.nih.gov
You probably also suffer under the false assumption that gabapentin affects the GABA receptor, it doesn't, at all. Yes, gabapentin does increase levels of GABA in the brain but it does that independent of activity at the GABA receptor. It's a downstream effect from its action at the alpha-One-Delta-2 receptor.