[DISCLAIMER: I have not personally done odometry in the past, but I plan on working on it this year. ]
Odom and PID are two separate things. Teams who use odometry often use the values from it for the error portion of the PID*, but the PID controller does not care where it gets it’s inputs from. A constant value works just as well, it is just not as precise or adaptive.
*Odometry is just a type of position tracking, and as such you can’t just input the values from odom into the PID, you need a motion control algorithm (pure purse, RAMSETE, etc; look these up on the forum) to actually use the information the odometry program provides.
If PID or odometry is new to you, I would start with the thing you know, and experiment with the one you don’t. If both are new, try out PID first. If you know both, implement odom and try out motion control algorithms.
As for your bonus question, there is nothing stopping you, so go for it. I think a lot of teams will do this, or something similar.
I do not know what your experience has been with odometry, but with good quality tracking wheels and under-control driving, I would think your position would still be accurate enough.
The v5 distance sensor only has a max range of about 6.5 feet, and the ultrasonic rangefinder has a max range of about 9.5 feet (numbers per their product pages), although I doubt they would be precise enough at that range to be up for the task. In my experience with the vision sensor, I do not think it would be accurate enough for a targeting script, but I would love to be proven wrong.