Yes. The BOSS GX-100 supports acoustic-electric guitar input. The GX-100 features an AC RESONANCE effect, which adjusts the pickup sound of an acoustic-electric guitar to produce a full-bodied, microphone-like tone.
Set the input level to match the output level of the acoustic-electric guitar. Refer to "Configuring the input to match the instrument you connect" in the GX-100 Reference Manual for details.
For AC RESONANCE parameters, refer to "AC RESONANCE" in the GX-100 Parameter Guide.