recording piano or connecting stagepiano via midi?

[merlino]

Dear musician's

If you connect your keyboard/midi piano/stage piano etc via MIDI and you select one of those nice piano's for example the piano's by native instruments, and you record midi, are those notes that appear in REAPER of the same accuracy as you just record audio?

for example, if i press 1 note with my finger, does that note appear at the same time as i press it if I set the latency to the lowest possible?

I wanted to make some recordings and video them, so it might be useful that I can use MIDI as a real accurate and solid instrument.
thanks !