It could work, but how many troopers are going to burn up their blaster in the process, and if they don't kill him, then the Jedi is unopposed.
An energy based weapon must build heat much faster than a kinetic weapon, and have you ever seen what happens to an M16 when you fire it continuously for a minute straight? There is an episode of Sons of Guns where they water cool an M16 to be mounted on a boat, and the effect of just thirty seconds of continuous fire on the unmodified rifle is amazing. The effect on a blaster rifle has to be way worse.
That is what everyone keeps forgetting. Yeah, I could go all Rambo on him with an M60, but if the Jedi avoids it for long enough, I burn up the barrel and then I am defenseless. M60s are designed for that type of fighting, and they still only get about a minute of continuous fire before the barrel is destroyed.
If you build a faulty lightsaber, the blade will eat through the hilt and explode, causing you to lose an arm, if you are lucky. (*Cough*Tenel Ka*Cough*) If we all agree that Blasters and lightsabers are similar technology, obviously you have the same limitations as far as building the barrel and firing chamber, and overheating either of those ends catastrophically.