Safe is relative. I've done both, and with the hole drilled near the ends of the drops there's a bit of a ridge of cable under the bar tape, but more peace of mind that they're not about to fall to bits.
Tape the cable from the hole up to the shifter. You don’t need to tape the entire length, just enough to keep it in place. The bar tape then covers the entire cable.
Safe is relative. I've done both, and with the hole drilled near the ends of the drops there's a bit of a ridge of cable under the bar tape, but more peace of mind that they're not about to fall to bits.