For the classical analog wired telephony lines, the human speech bandwidth is taken to be in [300 , 3000] Hz. This range can be extended by different similar applications such as wireless handsets, voice over IP, streaming apps, and GSM.
Most probably GSM also takes human speech range to be in the similar bandwidth, although later mobile phone standards 4G/4G+ etc also support higher quality voice services and hence consider a wider speech bandwidth.
Your understanding of modulation is basically correct for classical analog continuous wave amplitude modulation (AM, DSB-SC, SSB etc) in which a carrier cosine wave amplitude is continuously controlled by the instantaneous amplitude of the message signal which is voice in this case.
However, GSM for cellular phones employs a digital modulation scheme. Hence it's sending bits instead of continuous amplitudes. Note that it sends the bits not as 5V or 0V states (like it's in a digital computer wire), rather it still uses sorts of sine wave packets whose various attributes are used to convey the digital information. Other digital modulation techniques also exist.
Furthermore and most importantly, GSM is not sending the waveform shape of the input speech; rather it transforms the input speech into a compressed form (using LPC type of voice coder) and sends those bits instead.