No. Plan perks like unlimited text prompts and daily image limits refer to use inside the Venice web app and mobile app, not the API.
API usage is metered separately. Every API call consumes credits (or charges your balance) based on the model's per-token price, regardless of whether you're on Pro, Pro+, or Max (API calls can use the credits allotted through your monthly plan though). Paid plans do not include unlimited API usage.
If you use a text model via the API and see your balance going down, that is expected. Even for models that are free inside the web app, API calls are billed per token.
You can find the per-model API rates at docs.venice.ai/overview/pricing.