Yes it does, but it is not always reliable, especially if you have more than one remote paired to the Wally. For example, when you turn on the Wally, it may display a low battery indicator, but that may not indicate which remote it is reading the low battery strength from. This may happen, for instance, if you use an older-model IR Dish remote, or some other universal IR remote, to turn on the Wally. It can only read the remote battery strength from the newer-model Dish remotes that are "paired" with the Wally, but then you still have to go to the Diagnostics screen to see which remote may be causing that indicator. Then, on that screen, the battery strength indicator may say that the batteries are just fine, even if they are actually starting to get weak.
With a completely unresponsive remote that still lights up, there is another issue that may happen where the remote seems to stay "stuck" with the lights on. (This is especially true for the 54-series remotes with the backlight.) In this case, simply removing the batteries and re-inserting them (or removing only one battery and re-inserting it) will get the remote "unstuck" so it will start working again. This issue may also indicate that the batteries are starting to get weak. However, they still have enough power to actually control the receiver just fine for quite awhile.