I suggest you try it and see if you think it serves your work well. I’ve used borders on my website’s BW images and think they serve the images well, but I was able to load several images with different borders and keep them hidden from public view until I was sure I had something I liked.
My border is 95% gray. I use an action I made in Photoshop which is automatically started as part of the export process from Lightroom.
I don’t know how much choice you have in choosing the background color for your images, but the choice of border tone would be related (subjectively, of course) to that.