Will running a de-humidifyer next to my oil panting dry it overnight?

Answer 1

No.
Oil paint "drying" is as much about curing and hardening as it is about evaporating the solvent. SInce the paint is not water-based, relative humidity doesn't have much if any impact upon evaporation of solvent. The linseed (or other drying) oil base forms a tough polymer over time upon exposure to air and light. This hardening, or curing typically takes from days to weeks to complete.

Using boiled linseed oil and using certain additives can accelerate this somewhat, but the basic principle is the same.