Driver distraction remains a leading contributor to motor vehicle crashes, necessitating rigorous evaluation of new in-vehicle technologies. This study assessed the visual and cognitive demands associated with an advanced Large Language Model (LLM) conversational agent (Gemini Live) during on-road driving, comparing it against handsfree phone calls, visual turn-by-turn guidance (low load baseline), and the Operation Span (OSPAN) task (high load anchor). Thirty-two licensed drivers completed five secondary tasks while visual and cognitive demands were measured using the Detection Response Task (DRT) for cognitive load, eye-tracking for visual attention, and subjective workload ratings. Results indicated that Gemini Live interactions (both single-turn and multi-turn) and hands-free phone calls shared similar levels of cognitive load, between that of visual turn-by-turn guidance and OSPAN. Exploratory analysis showed that cognitive load remained stable across extended multi-turn conversations. All tasks maintained mean glance durations well below the well-established 2-second safety threshold, confirming low visual demand. Furthermore, drivers consistently dedicated longer glances to the roadway between brief off-road glances toward the device during task completion, particularly during voice-based interactions, rendering longer total-eyes-off-road time findings less consequential. Subjective ratings mirrored objective data, with participants reporting low effort, demands, and perceived distraction for Gemini Live. These findings demonstrate that advanced LLM conversational agents, when implemented via voice interfaces, impose cognitive and visual demands comparable to established, low-risk hands-free benchmarks, supporting their safe deployment in the driving environment.