#YES

There is nothing about the Ethereal Plane (Border Ethereal) which would in principle prevent you from having a long rest; however creatures who live on the plane or travel through the plane might disturb your rest, e.g. a Ghost or a Phase Spider.

Since you intend to rest, once you are in the Ethereal Plane, you could cast Rope Trick (PHB p.255) for a short rest or Leodmund's Tiny Hut (PHB p.272)for a long rest, just to increase your chances of your rest not being disturbed. You could use it on the Material Plane as well, but I'm guessing there is secondary reason for using Etherealness as this is a 7th level spell and Rope Trick and Leodmund's Tiny Hut are respectively 2nd and 3rd level spells.

YES

There is nothing about the Ethereal Plane (Border Ethereal) which would in principle prevent you from having a long rest; however creatures who live on the plane or travel through the plane might disturb your rest, e.g. a Ghost or a Phase Spider.

Since you intend to rest, once you are in the Ethereal Plane, you could cast Rope Trick (PHB p.255) for a short rest or Leodmund's Tiny Hut (PHB p.272)for a long rest, just to increase your chances of your rest not being disturbed. You could use it on the Material Plane as well, but I'm guessing there is secondary reason for using Etherealness as this is a 7th level spell and Rope Trick and Leodmund's Tiny Hut are respectively 2nd and 3rd level spells.