Dark Object Subtraction using Top of Atmosphere Reflectance?

Dark object subtraction is not atmospheric correction. It is image normalization. It is the simplest way of making two images acquired at different times, with different atmospheric conditions and view angles resemble eachother spectrally.

As such, what you get is not a 'correct surface reflectance value'. What you get is something that may, or may not, help you compare images from different times.

With the above in mind, yes, you would get 'DOS-corrected surface reflectance values' from that approach, but they should not be used for physical modelling or comparison with reflective spectra from the literature, as these things require actual atmospherically corrected data.

With your edits in mind - yes, DOS correction can be done on TOA reflectance data, and you simply do it by finding one or more dark objects and subtracting their value (or average value) from the original TOA reflectance. You should also consider what impact negative values will have on your further use of the data, and if they should be set to 0 instead.