Heavens NO! I vacuum rarely enough as it is, if I did that I'd feel like I have to vacuum after every sewing day ;-)
I have a small basket on the table that I put thread and super small fabric cuttings, and paper from paper-piecing. I just empty it into the trash can in the kitchen.
If I have a very long piece of thread (from doing something dumb) I might put it in the sewing box to use while hand sewing something at a later date. (I did that a couple times then asked myself if I'd be able to lay my hands on it later to use it, or if it would be the right color so I haven't done that again)