We present an empirical study of how far general-purpose coding agents -- without hardware-specific training -- can optimize hardware designs from high-level algorithmic specifications. We introduce an agent factory, a two-stage pipeline that constructs and coordinates multiple autonomous optimization agents. In Stage~1, the pipeline decomposes a design into sub-kernels, independently optimizes each using pragma and code-level transformations, and formulates an Integer Linear Program (ILP) to assemble globally promising configurations under an area constraint. In Stage~2, it launches $N$ expert agents over the top ILP solutions, each exploring cross-function optimizations such as pragma recombination, loop fusion, and memory restructuring that are not captured by sub-kernel decomposition. We evaluate the approach on 12 kernels from HLS-Eval and Rodinia-HLS using Claude Code (Opus~4.5/4.6) with AMD Vitis HLS. Scaling from 1 to 10 agents yields a mean $8.27\times$ speedup over baseline, with larger gains on harder benchmarks: streamcluster exceeds $20\times$ and kmeans reaches approximately $10\times$. Across benchmarks, agents consistently rediscover known hardware optimization patterns without domain-specific training, and the best designs often do not originate from top-ranked ILP candidates, indicating that global optimization exposes improvements missed by sub-kernel search. These results establish agent scaling as a practical and effective axis for HLS optimization.