How far from the target are you? In my opinion you need to be shooting from at least twenty yards to get decent results, twenty five or thirty is even better.
The reason I ask is because I don't ever see bare shafts "fishtailing". There might be one correction at the start but then they plane off to one side or the other, or up or down. Fishtailing is caused by fletching correcting poor arrow flight, over correcting and getting in to a back and forth pattern.
The direct answer to your question is yes, when everything is right the bare shaft will fly like a bullet, straight to the target. In fact it's tough to see the bare shafts in flight when you get close, they are just a speck going down range.
If you are grouping bare shafts and fletched shafts together at twenty five to thirty yards, I wouldn't worry too much if the bare shafts aren't perfectly straight in the target. In a perfect world they would be, and you may well get them there, but bare shafts are very sensitive and if they are significantly off they will plane out of the group. Targets also magnify any deviation from perpendicular and may even impose a direction change due to being less than perfectly homogeneous.