I do remember a few years ago reading (I think it was in freakonomics) that this isn't actually a guarantee. Some places that have postal voting as the primary form of voting have actually seen a decrease in participation. After an initial boost based on novelty, it now being easier to do also makes it easier to put off. Having a week or two to fill in and then post the form allows for a lot of "I'll do it tomorrow" until you can't, you missed the cutoff. If it can increase turnout great, but making something easier doesn't inherently mean an uptake in participation.

As an extra method on top of existing options it would probably help, but then you lose a lot of the other suggested benefits around faster counting and etc. which require it to be the only form of voting.