I think that both the bags and the leaves can be used as mulches.

Brown paper bags, kraft paper, are processed less than other papers because the color of wood pulp is brown, the color of those bags, so yes they can be used (and I have) in your garden.
Tree leaves are a very good addition to any garden, much better than anything you can buy at a store. As these tree leaves are worked on by the Soil Food Web in your soil they will make your plants healthier so those plants can better withstand insect pests and plant diseases, so any disease they might have are not a concern. Maybe, possibly if the soil you currently have does not have a good, active Soil food Web, for a few years until that SFW does get working you may see some problems, about the same as anyone with a "conventional" garden soil would.

Thanks for the responses. I like the thought of free mulch.

I use paper mulches and in some of my beds, I apply them annually. If your mulch gets thin, add more paper or whatever else you've got right on top of your last year's mulch---leaves, compost, etc., in my case paper, seaweed, and hay or leaf mold for a pretty top layer. Strawberries like a pine needle mulch, if you have access to them. Southerners call pine 'needles' pine 'straw'. I'm a perpetual mulcher, so I like mulches that break down and nourish quickly. I despise commercially available wood mulches, so commend your figuring out a better way to mulch.

You may very well find a pest problem from your leaves---primarily slugs---but find a way to deal with them if you do---mulching cures more problems than it causes.