Is it possible to keep formulas when publishing an Excel file to ArcGIS Online?

No, the formulas in the Excel file are not retained. Instead, the values calculated by the formulas are preserved. This means that any dynamic calculations you had in an Excel file will be converted to static values in ArcGIS Online.

ArcGIS Online treats all data from an Excel file as attributes. This applies when publishing an Excel file directly to ArcGIS Online or when publishing using ArcGIS for Excel. Therefore, if you need to have access to the formulas, keep a copy of the original Excel file.