The short answer
No, within reason, and pretending otherwise helps no one. Investors do not want you distracted by money stress or burning out, and a founder who cannot cover their own life makes worse decisions. What they watch is proportion: a salary that comfortably covers your real costs is expected and fine; one that looks like you are extracting wealth before building it is not. Norms vary by stage and city, and many funds have rough guidelines. Set your pay to a reasonable, defensible number, put it in the plan openly, and revisit it as the company can afford more. Underpaying yourself into hardship is not the virtue signal it is sometimes treated as.
A curated summary to orient you, not advice. The resources below are the real value.