Emulators these days will process faster than the original consoles, so there is no lag there. The only lag will be the modern LCD (which depending on the size of the screen can be up to 2-3 frames at 60fps), which isn't the fault of the emulator. Most people will be playing through an LCD regardless of whether it's the console or emulated. My PC is still rocking an old 17" CRT, so no problem there for me!
I have every Atari 2600 & Lynx, Master System, and N64 game, and hundreds of NES, SNES, Genesis/Mega Drive, Gameboy/Advance, Amiga 500 games, and the emulated nature of them has never stopped me playing a game, except when my computer simply wasn't fast enough (not even an issue now, I can play Wii games at full 60fps without dropping a frame).
In fact, emulators often run faster than the console, making the game easier to play, unless the emulator accurately limits the processing speed to that of the console.
I do know that the more modern consoles are more resource intensive, so it requires more computer overhead to run the emulator on top of the game which can introduce issues (that's why there's no 360 emulator). Still, I can't imagine that an original NES requires much power to emulate the hardware.
That and the fact that modern console manufacturers are more aware of emulation, and will kick your ass for attempting to emulate their modern hardware. They now basically patent the hardware so that you're breaking the law for even emulating the hardware.
A NES isn't even a blip on modern hardware. My old P133 was running those full speed.