I would do anything I could to get air out of the cooling system. When you refill and let the engine warm to operating temp, watch for fluid level drop and add as needed. Very short road test and check again and add as needed. Make sure to check for leaks as well. You never know with a reman/rebuilt engine. Mistakes happen. So, no, I do not agree with whoever would say that "burping air" from the cooling system is not important.
We recommend that you put all your rig(s) info in your signature so we all don’t have to guess at year, make, model, engine size, trans, rear axle locker…….etc. While you may have posted pertinent info in your first post, you may forget to do it again and the info is needed by us anyway. Makes it way easier on all members that attempt to help, to have that info right up front. It is also recommended that you take a pic of your RPO codes, on the inside cover of the glove box, and post that image in your signature. All this info will greatly help those that will try to help with a problem.
If there is any other info, like upgrades, mods or recent mechanical/maintenance work done, that would be helpful in any post as well. Too many times a question is asked by the poster and after about 10 responses we find out that the poster has done recent work to attempt to fix the problem or work that was done that SEEMS not related to the problem.