Bore alignment with your sights is a critical element to long range shooting. It can be eliminated with sight adjustment. The more sight adjustment is less precise and predictable movement due to the sights moving in an arc instead of vertical or horizontal. The fix with an optic is super easy but would require some serious gun work with iron sights. How important is determined on how precise you want to be, but usually this is not a factor unless shooting very precise targets, longer ranges, and or an inaccurate gun. For me precise is .25 MOA or less, longer range +500yds, inaccurate +1 MOA.
In order to determine if your sights are actually not in line with your bore is pretty easy if you have an accurate gun...not so if you don't but can still be done. This will also tell you if your scope/sights are tracking true or not. Usually the quickest way to tell is shoot a 100yd target with true level lines on it. Hang a large sheet of clean paper. I use 4' wide paper rolls and just cut a square, and you can get this at any craft store or amazon. Get the thicker paper not thin...otherwise it tears easy and is just a pain to deal with.
I use a bubble level and make mark a line in the center and vertical across it. I just use a magic marker so I can see it with my spotter/scope. My horizontal line is usually well below the middle because I always make a vertical adjustment. Mark or have your aiming point exact center on the line junction and shoot a group. If your gun is hyper accurate (.5" or less for me) you can get away with a single shot to adjusting but I then verify with a group. Aim exact at junction with cross hairs (optic) perfectly on your drawn lines. After the first shot/group make a large (Full turn optic 16-18"/two feet irons) sight adjustment in one direction. Shoot another group/shot with the exact same aiming point/aligment. You will see instantly if or how far off your sight to bore alignment is with the second group. Draw another line from the fist shot/group center to the second shot/group center.
To correct it with a scope is easy. Just hold/lock the rifle in position with the same aiming point and the cross hairs exactly on the original lines. I just put sand bags on my fore end/barrel against the rest and same for butt stock. Loosen the scope and turn it until the vertical is perfectly in line with the offset line you just drew and tighten back down. Verify with some more shots and adjust as needed. Then attach your bubble level to your scope or rifle and your sights/bore are in line.
To correct the most precise way with irons would require an actual sight movement on a arc. So if you had a round receiver you could have the base holes off set or drill new receive holes, and if flat has to be the round barrel sight moved. The problem would b...how much?? You could lean the rifle over from the original vertical until the sights are lined up and measure, but maybe there is a math formula (sure there is but have to find it) to determine how much it needs moved. Just remember it has to move on an arc...flat will not solve your problem. Also, move rear sight the direction of your second group and front sight opposite direction.
Hope the info helps.