That's what I did! I think it makes a lot of sense. Even though it seems expensive up front, it allows you to do a 5-wheel rotation (if you keep up with rotations regularly), effectively extending the life of a set of tires. It also allows you to keep going after a flat without interrupting your schedule to find a tire shop ASAP. Certainly not necessary, but this is probably the safest option... So does it make sense? That's up to you, but IMO, Peace of mind = priceless.
Or 1/16"

there is no one correct answer, it depends on how new your tires are, if you only have 4,000 or 5,000 miles on them is a totally different answer than if they have 20,000 miles on them.
Actually, number of miles on the tires might not tell you much about how much they're worn. Depending on the type of tires, road/trail/track conditions, and the driver, it's possible that 20,000mi tires could be worn less than 5,000mi tires. The only sure way is to
measure them, or have them measured if you can't do it by yourself.
The fact that the cost-saver spare tyre is a few inches smaller in diameter than the normal tyre gives the lie to the need to match tyres within fractions of an inch.
As has been mentioned, this is dangerous advice. The differential can handle tires of uneven diameter for TEMPORARY periods, but it adds a lot of strain. Please follow the recommendations in your owner's manual, which are as Josh stated:
put spare on rear only (swap with front if necessary)
low speed only
minimize distance driven on spare
Be safe, and be nice to your car!