Yes, it's okay for both parents to sleep at the same time, for several reasons.
The human mind is finely tuned to the sound of crying babies, you'll be surprised at what you can hear subconsciously while you sleep. Our pediatrician wisely commented that newborns have only one desire - to grow older - so you can be sure they'll tell you if something is bothering them enough.
Another reason to sleep together is that parents need to take care of each other too. If you always put the baby first, then you'll burn out. You can only care for the baby when you're adequately reasonably sort of rested and balanced.
The only situation where "keeping watch" might be sensible is if you're very worried about SIDS. The problem is that "sudden" really means "science has no idea what causes this and there seem to be no symptoms", so nobody can say if this child is more/less at risk. For parents that are worried specifically about SIDS there are products like Angel Care but mostly you've just got to accept that you can't prevent some things. Also, as KennyPeanuts points out, SIDS is very rare and often misunderstood to include suffocation from objects (teddys, pillows, blankets) so be sure to have a safe crib those first few months.