Not likely!
Well, as a resident of the Australian (some would say Penal) Colony, I can tell you the reference to 8 people dying in Australia from battery-to-the-tounge-syndrome is rubbish.
Gored by a kangaroo, eaten by a crocodile...perhaps. 9v batteries - nope!
Unless someone has a pacemaker, I believe it not to be possible regardless - except maybe if they had some seriously weird heart condition.
The method of death referred to, involving the nerves revolves around nerves becoming depolarised. When this happens to a significant extent they can not recover.
This is actually the primary method by which criminals are electrocuted (mostly still in the US only) in electric chairs. The secondary method is a lovely cooking of the quite a few of the internal organs beyond the temperature at which they can function (or ever function again).
The present method for electrocution in Florida is as follows:
2,300 volts, 9.5 amps, for 8 seconds; 1,000 volts, 4 amps for 22 seconds; and 2,300 volts, 9.5 amps for 8 seconds. Other states vary. Some like to cook you at 480 volts for 10-15 minutes at the end!
The actual figures vary slightly per "customer" due to differing fat levels etc which effect the resistance. It is typically acknowledged that the first zap does nor depolarise the nerves fully.
Its worth noting that those figures do NOT guarantee success. There are many instances where it has failed to do the job, and thats despite excellent saline conductors to the top of the head and a nice engineered exit path via the ankle.
As you can see it would be pretty hard for a 9v battery to come even close with a "typical" person!
The actual current needed to permanently depolarise nerves is generally agred to be around seventy-five milliamps (75/1000 of an amp), externally applied to the body causes fibrillation of the heart. One amp of current applied externally to the body is sufficient to cause the heart to stop completely.
Whats interesting is that, for example, a duracell 9v battery can peak around 200milliamps - well above the 75milliamps that can end your life. But the natural resistance of the human body is typically between 2,000 and 50,000 ohms, which massively drops the current. Its this same resistance that would likely let you get away with touching the terminals of a car battery while the engine is being started - and 200+ amps are being sucked out of the battery.
The tongue would improve that by reducing the resistance (if you remove the skin, it drops to 500ohms), but not to the extent that you would likely have enough current reaching your vitals to harm you. But in general if you wanted to really reduce the resistance, you would need to apply the shock right in the middle of your chest, quite near your heart.
By the way, a detailed account of the incident with the ohmmeter and 9v battery can be read here: http://www.darwinawards.com/darwin/darwin1999-50.html
I believe it to be an urban myth as even if he stuck them in his thumbs, there would still be considerable resistance between his thumbs and his heart. Now if he dug them deep into his nipples...that I may be able to believe! (Sort of...)