There is no current tube spec that calls out such properties. The 1/8, 1/4 hard and so on from the sheet specs do not directly apply to tubing.
Yes you can get cold drawn as drawn tubing in virtually all SS grades.
Different mills will call out different tensile properties, usually min only.
Unless you have a tensile that you want.
We do a lot of this at Plymouth Tube, Trent mill.
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Plymouth Tube