A helping hand
To answer your questions, yes and yes.
The IC706MKIIG is one fine radio. A member of the DC-to-Light radios being manufactured by almost all, Icom, Yaesu, Kenwood, etc...
The receiver selectivity makes these radios exceptionally good for DX listening. They pretty well ignore adjacent signals, far better than anything built for the dash of a vehicle.
Since the antenna input is a 50 ohm impedance, you will want to use an antenna tuner to help change the high impedance of a very short whip (relative to the actual wavelength of AM signals) into the low impedance value of 50 ohms. This is not to say that even without an antenna tuner you won't hear lots of signals. But, a resonant antenna situation will work much better, AND you did say you want to listen for DX broadcast AM signals.
I was thinking about suggesting a ferrite loop antenna but that would only work in a fixed situation where you aren't twisting and turning following the highway. Ferrite loop antennas have a tremendous null capability to get rid of unwanted interference.
I have never messed with anything lower than 160 meters and at that, I used very long wires for my receiving antennas. I found some links that you can pursue and occupy your spare hours.
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http://www.mindspring.com/~brucec/dx.htm
Building Your Own AM Tuner
by Bruce Carter
http://www.mindspring.com/~brucec/amtuner.htm
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http://home.earthlink.net/~w9wi/
http://home.earthlink.net/~wb5rex/xtalman/literature.html
http://bellsouthpwp.net/w/b/wb9nme/
http://www.dobe.com/wts/resources.htm
http://www.angelfire.com/wi/dxing/
http://www.dxing.com/amband.htm
Best of luck,
John