I don't see any reason why the toy couldn't be programmed to immediately repeat any signal it recieves. The toy, at least, appears to be built for very nearly that exact purpose. Now, it's true that it's designed to work with a computer, but it can probably be repurposed to just reproduce the signal it'd just recieved with a little reprogramming.
As for the LED repeater, it's already programmed to do precisely that. Only much slower than you'd need. So there you'd probably just need to turn up the clock. As for range, banned, I don't know. Your range is a product of a dozen different factors: photoresistor vs. phototransistor, window material, window size, etc. etc. etc... Test it and find out. I mean, between both products you're spending a whopping $30. If you're attempting to build a product, then it's $30 of extremely valuable research. If you're just screwing around, you may very well learn a few things.
One caveat: This is an AVR board. I'm not saying there aren't people here who don't know their banned with PICs, but 90% of the discussions you're going to see about programming a micro are going to be spoken in AVR. I, for one, don't speak PIC at all. That might be a strike against the toy.
Red M&M, Blue M&M: They all wind up the same color