Yes, please follow the straight out instructions in ATIS (or the altitude given to you by the tower controller upon takeoff). Just because you tuned out of tower doesn’t mean you won’t hit any other aircraft by turning. :)
Edit: Keep in mind that you don’t necessarily have to fly to the end of the cone. The point of straight out departures is so that you maintain runway heading until clear of any traffic that you may collide with if turning.
As @TaipeiGuru said, you do not have to fly to the end of the cone (unless said in ATIS straight out departures only or when tower tells you fly runway heading until at or above XXXX feet). If a departure frequency is active, always listen to their instructions, but other than that, you can fly according to your flight plan.