I'm not exactly sure on the details of AES-GCM, but in general if you use secret data to influence either the data path (indexing tables), code path (branches)

I'm not exactly sure on the details of AES-GCM, but in general if you use secret data to influence either the data path (indexing tables), code path (branches) or timing (either branches or non-constant instructions) then your secret data should be considered compromised in a model allowing side channel attacks.