Now I don't know for sure; since I do not have RTR installed on my PC (I had once, but then my PC wasn't quite like what it is now - so the game refused to run battles period) -- and therefore I am not exactly up-to-date with the latest platform it uses.

In other words: find out for yourself.

Here's how:
EB 1.0 runs on RTW 1.5;
RTR from what I knew runs on RTW 1.2.

So if your release of RTR also runs on RTW 1.2 then it will not work with EB 1.0: the 'platform' does not match.

If, however, you run RTR on RTW 1.5 or later you should be able to install EB on top of that. (See the guide in the bugs&support forum if you do not know how to install EB.)

In any case: EB requires a clean RTW 1.5 install: anything below 1.5 will make the game not run; and anything above is not officially supported, but should work as well.

Clean means that you do not have anything that does not belong to standard RTW 1.5 inside the RTW 1.5 structure (excluding any data inside a so-called mod-folder: that is a folder named after the mod itself).

It is recommended to use a folder with a clean 1.5 build without any other mods installed, though. The reason is that other mods may not fully rely on their mod-folder, but replace a few other files in the main RTW structure. Nine times out of ten this should not make much difference; since EB uses hardly anything but the exe; dll-files and certain packs from aforementioned RTW structure. But it may cause weird bugs if both mods use the same element when one mod has replaced it with its own version.