Medicare Part A covers hospitalization. However, Medicare Part A does not pay every all of the out pocket costs from the hospital. For 2016, Medicare Part A requires Medicare Beneficiaries to pay a $1,288.00 Deductible. Part A will also require the Beneficiary to pay $322.00 per day starting day 61.
The Medicare Supplement Plan G does pay the Part A Deductible and the Part A co-insurance (the per day charges). So YES, the Medicare Supplement Plan G does cover hospitalizations. If you have Medicare and the Medicare Supplement Plan G, you should not have any hospital bills to pay.