This might depend on what the end use of this work piece is. But generally any oil, grease, coating, rust or mill scale should be removed before welding.

When pipe welding, special care is given to joint preparation from pipe cut to fitting prep to fit-up, especially when code welding. IF you are tig welding the root on a pipe weld, you need to get rid of all scale before welding.
In biotech and electronic applications, joint preparation is particulary critical. The ss tubing (which is orbital welded) needs to be free of burrs, oil and any contaminants and also must be completely flat and so a facing tool is used. In the electronic industry, tubing that is cut must be under an argon or nitrogen purge while cutting and prepping.
In aerospace, details (parts to be welded on tube assemblies) are usually machine and alot of care is taken to prep the part per stringent FAA standards.
Some alloys such as aluminum have to be completely free of any burrs, shaving and especially oil or grease to produce sound welds. I was taught that edge preparation IS one of the most important aspects of any metals joining operation.