For OpenAI: short answer is no. From what I've seen, their biggest expense is training future models. If they stop that (putting aside the obvious downsides) they'd still be in the hole for a few billion dollars a year.

This is based on what I've read here: https://www.wheresyoured.at/openai-is-a-systemic-risk-to-the... (big AI bear, for what it's worth)

edit: Well, if they shed the other expenses that only really make sense when training future models (research, more data, fewer employees ..) they would be pretty close to break even.