Visible Light Communication (VLC) uses light-emitting diodes to provide wireless connectivity in public environments. Transmission security in this emerging channel is not trivial. Chaotic modulation techniques can provide encryption directly in the physical layer based on the random-alike evolution and strong synchronization prospect given by deterministic chaos. In secure chaotic inclusion or embedding methods, continuous-time chaos oscillator models need to be synchronized via a coupling carrier. Here we present a first numerical simulation study for the impact of the variable delays induced by line-of-sight and non-line-of-sight multipath fading in complete chaotic synchronization. More precisely, we analyze a chaotic Colpitts oscillator that is simultaneously transmitting the carrier to several mobile receivers via nine spotlights. Such induced delays depend on both the receiver position and the carrier frequency, influencing the complete synchronization required in modulation via chaotic inclusion. Correlation values for several receiver positions and carrier frequencies are presented, examining the progressive emergence of the multipath effect and its impact on chaotic synchronization. We show that, for the chaotic oscillator and coupling applied in the defined room settings, complete chaotic synchronization can be achieved and that it is robust up to the tens of MHz region.