Calabria, I agree with what Andy said but would like to drive down a little further into the topic. I would like to think I have studied this topic in extreme detail and hopefully can answer your question.
The first thing you have to do is understand that not all "organic" is equal. There are several organic methods that many practice:
1) Using an inert media such as promix, sunshine or some peat based medium and adding bottled organic nutrients. This is probably the most common method.
2) Using a bagged soil which is comprised of various peat, compost, rice hulls, vermiculite and such but that also includes many organic amendments as well such as fish meal, bone meal, etc. Some may or may not add more bottled organic nutrients or various other organic amendments to this as the grow progresses. This is probably a close second to the first path.
3) Using a true soil, one which is created by the user or someone with a good knowledge base on how to build a soil from various components such as peat, vermiculite, rice hulls, perlite, and many other amendments. This is closely related to path 2 except the grower will probably have a higher knowledge of how the soil/plant symbiosis works. This is one of the lesser paths that normally requires some skill to develop and nurture the soil.
4) Some use organic nutrients in hydro but I won't discuss that as your question seems to relate specifically to a medium other than water based. If you would like further explanation on this subject, ask, and I will explain in more detail. I have grown this way as well.
So, now that we have established the various ways an organic gardener can grow we can isolate each and how pH will affect them., referring back to the original numbers.
1) Your medium will probably have a fairly stable pH of 6.6 - 6.8 and enough buffer in it to keep the pH in that range throughout the grow. If you are adding strictly dry amendments to this medium then you shouldn't have to concern yourself with pH. If you are adding bottled organic nutrients to this base you may want to check the pH of each feed after you mix with water. In most cases, your pH probably won't be too far from 6.0 - 6.6 and in those cases there should be no need to adjust pH. If you are using a liquid silica, or some form of rhino skin or something like this then it would be imperative to adjust pH because of their high alkalinity, in some cases I have seen them as high a 14.3 out of the bottle! This can throw your pH way out of balance. For the most part though, if using a standard set of nutrients such as GO Box or

Trio you should still be fine with those in an inert medium.
2) Here is where I see most growers, especially new ones have problems. You have a powerful soil in terms of nutrients. Many bagged soils are pretty "hot" and all of these nutrients contained in the soil does affect pH and in many cases causes it to become acidic. Using straight water throughout the grow and most growers will be OK without checking pH IF the soil is of good quality. Many times, for the past few years we have seen

out of the bag vary wildly in pH and should be tested continuously. My opinion, there are very few bagged soils that are of good quality. Especially with the explosion of the indoor growers the past few years, manufacturing hasn't been able to keep up and quality has been slipping for years. Now, if you begin adding nutrients to a soil already packed full of nutrients then you are definitely going to have to test pH regularly and adjust as needed. More importantly and specifically, adjust feed water and not soil! Applying liming agents and such simply isn't going to help with your soil. Lime is meant to be a long term solution to soil acidity and given the fact that we are growing short season crops there isn't enough time to adjust soil pH. So, the only thing you can do is try to correct the feed water and give the plant a "liquid" pH in the correct range to allow her time to absorb those nutrients. Once the liquid has dried from the soil, your pH is back to where is started or pretty close and in some cases possibly worse if you are feeding a lot of excess nutrients.
3) Lastly, my favourite way to grow. True soil if created by an experienced soil builder, will be/should be close to the correct pH and should contain enough buffer in it to hold that pH throughout the grow. Here is the KEY, created by an experienced soil builder! There are a lot of recipes that are out there that are just guess work. Most of them are that way. For me, with my recipe, I have never and will never pH my soil. Here is the catch though, I ensure my pH is proper when I build the soil and I ensure that I have enough base buffer to keep it set throughout my grow. Also, I don't add any bottled nutrients to my mix throughout the grow. Adding more nutrients to the soil than is needed is going to throw your pH out and would need to be checked regularly to adjust as necessary.
So, sorry for the long explanation but hopefully that gives you a better understanding of natural or organic growing and pH. Anyone that says you never have to adjust pH is either trying to dumb things down or is dumb. pH is an important factor in all growing, regardless of organic or chemical. Can it be easier in organics? Yes, once you are sure of everything you are using and how you applying nutrients. It can be. Even then, it is an important tool to have in the chest for if/when you run into problems.
Best of luck on your journey my friend! Wishing you much success in your growing endeavours! There are several of us here that adhere to "true organic" principals and we are always available to answer questions.
@DubV ,
@Eyes on Fire and myself to name a few. Feel free to PM anytime.