Are bread improvers really needed?
The bread improvers that I have seen simply encourage gluten development to improve bread texture. They are often called for for use in bread machines because those machines are not as effective at kneading. Many bread improvers are as simple as extra vitamin C.
Without knowing the details of the machine you are planning to use it is difficult to say whether a bread improver would help. I would try without it. If the bread is too crumbly then add some Vitamin C.

Bread improvers do not change the flavor of the bread so much as the texture. I don't think the slight change in acidity would make much difference to the shelf life but I've not read anything about that.

Whether bread will mold in one day depends greatly on how the bread is stored and what you climate is. If it is very humid and the bread is stored uncovered then it could possibly mold after one day. If the climate is too dry then the bread could be quite stale after a day. 
There is a reason that preservative-free bread is usually sold the same day it is baked.

Note although not part of your question, brown sugar (and the soda to neutralize the brown sugar) are not at all required for bread to brown. A quick search for pita recipes shows either no sugar or just enough to activate the yeast in the recipe.