No reason not to shoot it, and they are great rifles.
Now, I am unable to assess the shootabillity of your rifle at long distance (crystal ball is in the shop for calibration and oil change), so do the next best thing- find a competent gunsmith, and have him check your rifle over. He will be looking for signs of damage, mising parts, anything that has been "Bubba'ed", condition of chamber/bore/muzzle, and the headspace of the rifle. Should only cost you a few $$$, and is decent insurance.
PLEASE avoid the temptation to put a synthetic stock on your rifle, drill and tap for a scope, etc. That is HERESY to a collector!
Some more info for you on your rifle- and congratulations!
Collecting and Shooting the U.S. Model 03A3 Rifle - HISTORY