What you're suggesting will, in my opinion, work fine - within its limits.
Let's say you have an 60 cm diameter wheel. At 60 mph it will be turning at 15 rps, so you don't need to worry about an extremely high digitization rate. 100 - 200 samples/sec should be adequate. Centripetal acceleration will be a major problem, since in this case (assuming a position 20 cm from the center) it equals about 177 g's. Superimposed on this will be your +/- 1 g sine wave (and the amplitude of the sine wave will not change with speed). So you'll need about 10 bits of A/D resolution to allow identification of the sine wave.
If you're still interested in the idea, there are at least three other concerns.
The first is the need to balance your wheel - if you don't, it will shake itself apart at speed. You'll need to dynamically balance it, not just static balance. Just like balancing a new tire.
The second is the question of how you're going to communicate the sensor readings. Slip rings? Wireless?
The third is shock and vibration: how do you expect to handle them? If you hit a rough patch of road, your package is in for a very nasty ride. Remember, it's on the wrong side of the suspension.
Alternatives - frankly, I'm not a big fan of mounting anything active on the wheel. I'd be more inclined to put a pair of magnets on opposite sides and use a magnetic detector mounted on the axle housing. Optical sensing is not a real great idea, since the dirt or dust kicked up by the wheels will be a problem, plus mechanically coupling it to the wheel/axle is not trivial.
EDIT Note - I'm assuming that this is not a fifth wheel, added expressly for the purpose of taking data, but rather that it is on of 4 "normal" wheels. If this assumption is wrong, modify my concerns appropriately.