Take the rocket equation :
v = ln(m0/mf) ve - g tburn
Where tburn is time to burn, v is velocity, ve is exhaust velocity, m0 is initial mass , mf is final mass
The Apollo third stage started its run to escape velocity at an altitude of 191km and speed of 8km/s. Per NASA.
Set Ve equal to the Saturn IVB exhaust velocity, or 4km/s. The fuel mass is 104 tons. Dry mass is 50t with payload. 475 sec burn time. G is 9.2m/s2 at 191km altitude.
Dv = ln(104/50t) 4kms - 9.2m/s2 (475s)
First term is
= 4kms (0.73)
Second term is
- 9.2m/s2 (475s)
= -4370 m/s
3kms - 4.37 kms = -1.37 km/s
The Saturn IVB would have a maximum velocity of -1.37 km/s which is far less than the earth escape velocity of 11km/s, and is still less even if we give it a 8km/s head start.