Yes it does have the heavy bull barrel SAVAGE A17™ TARGET THUMBHOLE
•Fluted heavy barrel contour
•Grey wood laminate thumbhole stock & vented forend A-SERIES COMMON FEATURES
•Semi-auto rimfire
•Straight Blowback System
•Thread-in Zero Tolerance Headspace System
•Case hardened billet machined steel receiver drilled & tapped
•Hard chrome bolt w/oversized bolt handle
•Dual-controlled round feed
•Bolt stop easily locks open
•User-adjustable AccuTrigger™
•Dual-safety trigger
•Blued carbon steel button-rifle barrel
•Includes 2-pc scope base & detachable rotary mag

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Yes, this model 17 has a 22" Carbon Steel "Heavy" Target Barrel.

Hi Timothy, Its 22" Carbon Steel Barrel Specifications and Features:
Savage Model A17 Target Thumbhole 47005
Semi Auto Rimfire Rifle
.17 Hornady Magnum Rimfire, .17 HMR
22" Carbon Steel Barrel
1:9 Twist
10 Rounds
Drilled and Tapped Receiver
Factory Installed Scope Mounts
Matte Grey Wood Laminate Thumbhole Stock
Overall Length 41.5"
Weight 5.41 Pounds
Satin Black Finish