In the NIST Special Publication 800-38D page #8 the maximum inputs lengths are defined in the standards as;
The bit lengths of the input strings to the authenticated encryption function shall meet the
following requirements:
and in section 8.3 the number of invocations requirements for all implementations:
The total number of invocations of the authenticated encryption function shall not exceed
$2^{32}$, including all IV lengths and all instances of the authenticated encryption function with
the given key.
- As a result, the recommendation doesn't advice the overflow of the counter.
We can find the maximum as:
$2^{32}$ invocation, per invocation you can encrypt 128-bit ($2^7$-bit) with AES, thus
$2^{32} \cdot 2^{7} = 2^{39}\text{-bit} \approx 68.7\text{GB}$ is the maximum data that one can encrypt with AES-GCM under the NIST recomendation.