Does an Enlisted Army soldier receive an automatic promotion to E-4 upon the completion of a bachlor’s degree?

Not automatically to E4 but they can put in as an E4 if you choose to use you college credit and with a degree you can also go in as an officer!

(Join to see) Are you currently thinking about joining the Army?

https://www.thebalance.com/advanced-paygrade-rank-enlistment-programs-3344738

No, automatic promotion to E4 is not authorized for completion of a bachelor's degree. However, there is an enlistment incentive, which I believe is still active, that allows one to enter the Army at the E4 pay grade if they hold a bachelors degree. This is only a policy though and can change at any time. You'd have to verify with MEPS / a current Army recruiter.