Yes, posture that prevent overstressing your back, injured or not, is important. 
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I might take a lot of heat from many people, including other physical therapists, for saying this but as humans, we are bound to slouch and have poor posture numerous times a day and it is not possible to maintain ideal posture 24 hours a day. I am saying that as a human.

Now, as a physiotherapist...

Ah, Pain...It's the cause of so many frustrations and discomfort and can seem life ending in some situation... Even when being explained the source of your pain by a medical professional, you still can't always explain it. And many patients don't understand how the site of their injury still hurts even though the tissue has healed.
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Over the past 20 years, the medical community has made great progress in understanding the multi facets and layers of pain, and with the help from researchers in pain science, the now more accepted model of describing pain is the biopsychosocial model.  In short, pain is seen as an interaction among and within the biological, psychological and social factors, unique to each individual.