I'm not an archer, however, I would be surprised if you would not notice any difference with your backpack as compared to no backpack – at least in the beginning.
Basically with every skill that requires precise and coordinated movement of your body the precision is more or less strongly susceptible to changes of the situation in which it is performed. This is due to the fact that our body is storing movements that it has learned and performed on a regular basis as so-called engrams, which can be compared to the code of a computer program that performs a certain task. Those engrams have a self-reinforcing character: every time you perform a movement that is stored in an engram, it gets refined and allows you to do a movement more precisely.
The downside is that changing an engram is harder than establishing one. This is the reason why it is rather time-consuming to practice and change a technique that you have learned and got used to in a different way. If you ever have learned any sports skill "wrongly" – by just doing it as you thought it should be done until it sort of worked – and later on tried to learn it "correctly", i.e. in the way it is typically done, you will know that this can be rather frustrating. In the beginning of such a change, it does not work at all and it can take a long time until you get the same results with the new, "correct" technique and you have to really take care to not fall back into old habits.
So, what does that have to do with your backpack? Well, you have learned shooting without a backpack and suddenly wearing a backpack can change some key aspects of your shooting. For example, your posture might have slightly changed due to the weight or maybe because you feel a bit impeded by the shoulder straps (this can even be unknowingly) or whatever. Basically it's just that the engrams that ensured before that you shoot precisely do no longer work as they were, since the parameters have changed and it might take some time and sessions to get used to this new situation. The good news is, I would expect way less time to adapt to the new backpack situation than what is needed to change a long established "wrong" habit, since in your case your engrams only need some slighter readjustment.
So, yes, I'm quite sure, you will get used to it. As a benefit, practising to reach a comparable level with the backpack might also help you to better adapt to varying conditions in general.