I think the answer is, Yes it certainly can. Is it likely?
Electric toasters work much the same way as space heaters or hair dryers, in that they run a current through high electrical resistant wires to generate incredible amounts of heat.
Most toasters tend to use Nichrome (alloy of 80% Nickel and 20% Chromium).
Electrical resistivity at room temperature:
1.0 × 10−6 to 1.5 × 10−6 Ωm . The Nichrome wire typically under this heat will react with air to be chemically stable meaning it forms an outer layer of Chromium Oxide which has incredibly high electrical resistance. If this isn't enough then in modern toasters these wires are coated with Mica which can provide enough resistance from the point of the coil to the knife where current will not ground through you.
Knowing all of this it is safe to assume that simply touching the wire with a knife while current is flowing will probably be okay. While the voltage is about 100-115 it will hurt, but the current travelling through is high to generate heat and certainly high enough to risk injury or death (Source: http://www.allaboutcircuits.com/vol_1/chpt_3/4.html).
Jabbing at the coils can risk flaking away the protective Mica or Chromium Oxide to make such a thing dangerous. Furthermore jabbing inside a toaster and making contact with the wires connecting the coil can certainly electrocute you however these are typically tucked safely away where you couldn't reach it with a knife unless you disassembled the body. (Source: http://www.straightdope.com/columns/read/2119/is-poking-a-knife-into-the-toaster-really-dangerous)
The other electrical components if applicable are probably feeding a circuit board and shouldn't go above 5 volts typically. There is no danger from jabbing the circuit board if that happens to be exposed, unless of course if you were to touch the timer relay which could cause a great amount of current to flow through you. (Source: http://www.wisegeek.com/what-is-an-electrical-relay.htm)
So basically, if you are viciously jamming a knife into a toaster, thats plugged into an outlet that doesn't have polarity or proper circuit breaker protection, and you are barefoot, then yes you certainly run the risk of electrocution or death.
EDIT: I forgot YET ANOTHER possibility of electrocution! If through the process of jamming an object into the device you inadvertently cause the toaster to short through the aluminum or steel internal casing, and the ground wire for the casing has been damaged OR the outlet is not grounded or not properly grounded... then YOU will become the ground! (Source: http://en.allexperts.com/q/Electrical-Wiring-Home-1734/Dangers-Ungrounded-Outlet.htm)