At least for the GitHub Flavoured Markdown, you can give the illusion by making all the non‑header row entries bold with the regular __ or ** formatting:
|Regular | text | in header | turns bold | |-|-|-|-| | __So__ | __bold__ | __all__ | __table entries__ | | __and__ | __it looks__ | __like a__ | __"headerless table"__ | | Regular | text | in header | turns bold |
|---|---|---|---|
| So | bold | all | table entries |
| and | it looks | like a | "headerless table" |