Battleplans?

Nope. AFAIK, this is a feature that will be introduced in Hearts of Iron IV.
In HoI, they appear to be purely cosmetic.

No Battle plans are mainly meant for multiplayer games.

Or as a reminder for yourself what your grand plan is about.

I use them to create "borders" between army groups, so that they don't get accidentally mixed up.

They can also give you something to do while you wait for the first couple of years leading up to the war.

I mainly use them to remind myself of the paths I've planned for the different units, so that my mounties don't end up in a city and my panzers don't end up in a forest. Especially for games in the Pacific, I also mark enemy provinces with naval bases, so that I know which islands to strike first. Also, I too make command "borders", so that I know how many units I have at my disposal for different operations.

I circle enemy provinces with strategic goals in green, provinces with important resoruces (especially rare metals) in yellow and the original borders in blue ... and also use the arrows (both, at the beginning of the war as well during progression) in order to denote directions of main thrust which are meant to encircle enemy armies (often in different colours to denote different armies/army groups)

Found it to be very useful, this way I have all important infos at a glance without having to switch between different displays (like the VP and the Resource display)

The only thing I am missing (to make the battleplan screen even more useful) would be Symbols that I can use for resources and VPs (symbols that are small enough to both fit into a single province ... unfortunately the symbols we have at hand are rather large)

I did use it once to map all the important provinces in occupied Europe, in order to see how many potential sites there were for strategic bombing and runway cratering. Turns out, there were about 75 or so, IIRC.

I use it to mark progress on the eastern front.

Or to mark where I've surrendered enemy armies and the amount of troops captured.

Or to mark other major events.

You need to document for the history books ya know