Intent-Based Networking (IBN) allows operators to specify high-level network goals rather than low-level configurations. While recent work demonstrates that large language models can automate configuration tasks, a distinct class of intents requires generating optimization code to compute provably optimal solutions for traffic engineering, routing, and resource allocation. Current systems assume text-based intent expression, requiring operators to enumerate topologies and parameters in prose. Network practitioners naturally reason about structure through diagrams, yet whether Vision-Language Models (VLMs) can process annotated network sketches into correct optimization code remains unexplored. We present IntentOpt, a benchmark of 85 optimization problems across 17 categories, evaluating four VLMs (GPT-5-Mini, Claude-Haiku-4.5, Gemini-2.5-Flash, Llama-3.2-11B-Vision) under three prompting strategies on multimodal versus text-only inputs. Our evaluation shows that visual parameter extraction reduces execution success by 12-21 percentage points (pp), with GPT-5-Mini dropping from 93% to 72%. Program-of-thought prompting decreases performance by up to 13 pp, and open-source models lag behind closed-source ones, with Llama-3.2-11B-Vision reaching 18% compared to 75% for GPT-5-Mini. These results establish baseline capabilities and limitations of current VLMs for optimization code generation within an IBN system. We also demonstrate practical feasibility through a case study that deploys VLM-generated code to network testbed infrastructure using Model Context Protocol.