Not exactly. The point is not to use paper bag, but to use durable/persistent bag from any material (even plastic) as long as you can.
For example, I almost never use one-time plastic bags, because I have backpack, so when I go to a grocery store, all the things placed into the backpack.
In such case (from energy perspective) it's easier to peoduce 1 backpack (32l) for several years of daily use instead of paper/plastic/etc ONE-TIME bag.
Unfortunately, that approach doesn't work with other things. For example, it's impossible to buy yogurt not in one-time plastic package and we didn't find a "mass market" solution to that problem. Same goes for any other ONE-TIME package