Okay so I've read through the IEEE Std 802.11-2012 documentation, and came to the conclusion that my concept is invalid and not feasible due to the following:
In section 11.6.2 of the IEEE Std, at the bottom of page 1249, the following statement appears:
If the GroupKey or SMK KDE is included in the Key Data field, but the Key Data field is not encrypted, the EAPOL-Key frames shall be ignored.
This rules out the option of sending an unencrypted GTK to the supplicant (client), knowing that sending an encrypted GTK to the supplicant is not possible as well due to the fact that the fake AP can't generate the actual (client-sided) PTK required for the encryption of the Key Data (including the GTK) in the 3rd EAPOL message of the four-way handshake.
The encryption of the Key Data field in WPA2 CCMP is usually achieved through the NIST AES key wrap algorithm documented in IEFT RFC 3394.
My assumption that the GTK could be sent to the supplicant unencrypted (before I arrived to that section of the IEEE Std) also ended up with a complete failure; it's further explained in section 11.6.6.4 of the IEEE Std 802.11-2012 on page 1259:
On reception of Message 3, ..., the supplicant also:
...
b) Verifies the Message 3 MIC. If the calculated MIC does not match the MIC that the Authenticator included in the EAPOL-Key frame, the Supplicant silently discards Message 3.
Again, since the fake AP can't generate a valid PTK, it can't calculate the valid MIC for Message 3, which results in a discarding of the message and failure of the operation.