If it's chronic back pain, and my back is not in a spasm, then yes, I workout around the pain. If I stopped working out every time my low back nagged me, I'd never work out.
I recommend you do these every single morning after you get up from bed...well, after you pee. It only takes a couple of minutes, but it works wonders for chronic low back pain.
those are some great movement, the first, I do everyday, huge part of what I HAVE to do to not feel my sciatic issues.
But... Stretching when you get out of bed is not good. I know, I know, lions do it so it must make sense huh? Not for us humans... Your core temp is low when you get out of bed, if really injured, your movement is kinda restricted and all. Why not wait until you have showered or have been up a for a bit? After a shower, if you do other kinds of stretches, you will notice you get more range.