IR Remote with Arduino
No, you can't use just an IR LED as the receiver.  While it is true that an IR LED can also be an IR receiver the voltages it generates are really really small. So you would need an amplification circuit. On top of that the TSOP1740 includes a band-pass filter to isolate the carrier frequency of the transmitted signal from the background light, which you would also need to implement.

So yes, while you could use an IR LED as a receiver, you need a large amount of support circuitry with it (which takes expertise not relevant to this website) to get it to do anything useful.