Is uke nagashi taught from punches as well as grabs? If so is it just taught from single jabs or combinations too? What kind of speed would an advanced Aikidoka train at? Does anyone have genuine experience of using uke nagashi in self-defence?
Short answer: Yes.
There are three core deflections used in "Tenshin" style Aikido. Uke Nagashi is one of them. However, in the video you referenced the instructor has a few terms mixed up, so if you are looking deeper into the subject, be sure to do some more research.
You are right about the natural reaction being like a boxer's guard, but the deflections are not meant to block, they are meant to, well... Deflect. The idea is to keep the attacker's momentum going and use their strength and power against them. Blocking will just halt the attack and reset the scenario.
The deflections do take a little getting used to, but once executed properly they work well. You can use the deflections against almost all types of attacks: tsuki, shomen, yokomen, jab, snap punch, round house, haymakers, kicks, grabs and combination attacks.