I have, from time to time, needed to drill deep holes in steel. Hence my collection of welded twist drills:
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Yes, it's possible to drill deep holes in steel with welded HSS twist drill bits. Some things to be aware of:
If you read old gunsmithing books, you will find extensive discussions of how to straighten gun barrels. That is because twist drills inherently drill curved holes. It is a result of the design of a twist drill.
Drilling deeper than the length of the flutes requires peck drilling to get the chips out.
Twist drills have large tolerances on hole diameter, even if the drill is properly sharpened. Reaming is necessary.
It's difficult to make straight holes with a gun drill. Gravity makes the drill shank sag, which causes the hole to curve upward. But a gun drill will make straighter holes than a twist drill, the diameter tolerance will be much tighter, and peck drilling is not necessary.
So, yes, it is possible. But do not expect to make match grade barrels.