I've done it both ways
It all depends on your location, but most newbies put far, FAR too much emphasis on cover. If a place is too busy to find another table quickly, I'll just say "Can't TAKE it no mo. You guys play without me this hand," and start counting my chips. (Next hand often stretches to half a dozen hands.) Natch, if they have NMSE you need a different plan.
Of course it's suspicious. You ARE suspicious. ;-) You think you're going to count, and win, over any serious period of time, and not have anyone suspect?
Never happen.
ETF
"When you wong out do u stay at the same table you were playing at and just continue to back count. Then once the count rises start playing again at the same table. Or do you move to a different table and start over?"