Does it make sense to train a convolutional neural network on lo-res, use on hi-res pictures?
When it comes to questions like this, you should be thinking about this in reverse. By that I mean, you want to actually use this algorithm at some point, don't you? So, the real question is: What do your images look like at prediction time?

Once you establish that, then what is the pre-processing you're going to be doing on these images? My guess is that you're not going to be changing things like the resolution. Sure, you might do some cropping or re-sizing, things like that. But the bottom line is that you should be training your algorithm based on what your prediction items are going to look like.