It all depends on what kind of spindle you have.
Mine was off an X2 mill and it certainly benefited from turning it. TTS was tight and difficult to remove. I turned the spindle nose and then they would just drop out like they are intended to do. I'd say if it's a Chinese mill spindle like mine was, do it. Without question. That is uness your tools currently just drop out by gravity when the drawbar is loosened.
Just get a cheap brazed carbide turning tool.
See here.
$3.89
This is the part number
3367A331
at
McMaster Carr.