A professional woodworker or furniture restorer may have better luck with tack cloth than an amateur who wants to stain one or two older pieces of furniture.
For example, it's hard to tell if a layer of paint or stain is dry enough for tack cloth. If it's not, using the sticky cloth could remove the paint or leave marks and might mean you will have to start over again.
If you're redoing a piece of furniture for personal use, it will most likely turn out just fine if you make sure all sawdust and other debris is removed after sanding and before painting or staining.
The effort and heartache saved will most likely be greater than the inconvenience of a speck of dust or two.