There's nothing wrong with trying, he might get lucky once or twice. That said, I'd highly recommend not giving him access to any special abilities or permanent benefits, although I wouldn't see it out of place to be able to train the Lightsaber Skill for attacks if he found a holocron or something.
Simply waving a lightsaber around gives him a candle's chance on Hoth of actually deflecting a blaster bolt, and so it shouldn't increase his Ranged Defense or give him any other abilities. However, if an enemy rolled a Despair against him with an energy weapon attack, the attacker could be hit in the same way that friendlies can be hit when firing into close combat.
This fairly represents his lack of the precognition that Jedi use to reliably deflect blaster bolts, since carrying the lightsaber does not increase his defense in any way. However, it also opens up the possibility of a lucky break, as a random bolt is deflected back at the opponent. Since most PCs would have to flip a Destiny Point to even get a Challenge Die into the pool, much less have a Despair come up, this would be a suitably rare and climactic event.
Also, since Force-based defensive abilities tend to involve upgrading enemy dice pools, representing lightsaber deflection in this way also reinforces the synergy within Force-Sensitive abilities.
Since Order 66 (as far as I know) is a standing order that's never been rescinded, at least the stormtroopers would know "Priority One = kill the Guy with the Glowing Sword"
Not necessarily. 0 BBY/ABY stormtroopers are largely conscripts, not indoctrinated clones, and I doubt the training academies focus on dealing with an extinct mystic order. The Emperor has Hands for that after all.
" In the event of Jedi officers acting against the interests of the Republic, and after receiving specific orders verified as coming directly from the Supreme Commander (Chancellor), GAR commanders will remove those officers by lethal force, and command of the GAR will revert to the Supreme Commander (Chancellor) until a new command structure is established."
Parts of that are kind of redundant now too There's no longer a Republic, a Chancellor, or a GAR.
That REALLY depends on what sources you're looking at. Star Wars: The New Essential Guide to Warfare still has them as elite troops, both natural-born or cloned (albeit they're still a step down from the original clones), and FFG's materiel is consistent with that portrayal.
And frankly, it hasn't been all that long. The standard setting for Edge is 20 years after Order 66, so almost every PC and NPC was born during the Old Republic. Many would have heard tales as children, some would have seen or even served alongside them. And although the specifics have been forgotten, the legend hasn't. Pretty much everyone from a planet capable interstellar flight should have heard rumors of the Jedi, and the lightsaber is their most distinguishing feature.
I totally agree with you about a lack of anti-Jedi training though. FFG even gives a nod to this, in one of the Objectives from their Star Wars LCG. #48 Self Preservation , includes the flavor text " Facing one of the few remaining Jedi was enough to give pause to even the most battle hardened soldiers of the Empire."