Burglar helps to pick and hack locks faster. It is necessary for covert passage.
I have played my PSI Sniper without Burglar since release. There was maybe a handful of times in three playthroughs were I did not have to abort the attempt and try a little later when a patrol came by or a random critter.
So no, it is not necessary for covert passage. At best it is quality of life feat and that is a generous assessment. If it at least would improve the skill for opening containers by let us say 10% or 15% I might be inclined to say it is useful at least.
