By RAW, Yes
TLDR: In order for the Ghost to be applicable to be effected by Turn Undead and Dispel Evil and Good, which their possession ability explicitly states that they are, then they by definition become applicable to be detected via Divine Sense and Detect Evil and Good. Via the fact that neither features or spells require you to target the Ghost directly, which is what possession protects the Ghost from. You can't have one without the other without inserting effects that possession doesn't grant.
Divine Sense and Detect Evil and Good have three requirements. Is the creature of a certain type? Are they in range? Are they not behind total cover? (or metal/stone/dirt in Detect EoG case)
The presence of strong evil registers on your Senses like a noxious odor, and powerful good rings like heavenly music in your ears. As an action, you can open your awareness to detect such forces. Until the end of your next turn, you know the location of any Celestial, fiend, or Undead within 60 feet of you that is not behind total cover.
Detect Evil and Good
For the duration, you know if there is an aberration, celestial, elemental, fey, fiend, or undead within 30 feet of you, as well as where the creature is located. Similarly, you know if there is a place or object within 30 feet of you that has been magically consecrated or desecrated.
The spell can penetrate most barriers, but it is blocked by 1 foot of stone, 1 inch of common metal, a thin sheet of lead, or 3 feet of wood or dirt.
Presuming a undead Ghost has possessed a humanoid and within range, then the only question remaining is, do they have full cover or not? The answer is no.
The ghost can't be targeted by any Attack, spell, or other Effect, except ones that turn Undead, and it retains its Alignment, Intelligence, Wisdom, Charisma, and immunity to being Charmed and Frightened. It otherwise uses the possessed target's Statistics, but doesn't gain access to the target's knowledge, Class Features, or Proficiencies.
The ghost disappears and cannot be targeted. This is not full cover, and at no point does the ability says or suggest that it is. The Ghost just cannot be targeted, and any damage or effect hit the host rather then the Ghost. (i.e. from indirect means, such as an AoE)
However, the possession ability explicitly states that the Ghost can still be affected by Turn Undead and Dispel Evil and Good.
As an action, you present your holy symbol and speak a prayer censuring the undead. Each undead that can see or hear you within 30 feet of you must make a Wisdom saving throw. If the creature fails its saving throw, it is turned for 1 minute or until it takes any damage.
Dispel Evil and Good
Break Enchantment. As your action, you touch a creature you can reach that is charmed, frightened, or possessed by a celestial, an elemental, a fey, a fiend, or an undead. The creature you touch is no longer charmed, frightened, or possessed by such creatures.
Meaning in the case of Turn Undead, the Ghost must be both present and able to see and hear the caster, as possession doesn't change the Ghost's creature type, thus it must still be an undead. Dispel Evil and Good only requires the Ghost to be present and of the Undead creature type.
Since we know the Ghost is in fact applicable to the effects of both Turn Undead and Dispel Evil and Good, when know for a fact that the Ghost retains its creature type and is still present even after disappearing during possession. The Ghost disappears and is no longer visible as opposes to the Invisible status. This is not non-existence.
Conclusion: As I have explained, Turn Undead requires the Ghost to still be present, in range and of the same undead creature type during possession in order to effect the Ghost, which they are. Possession doesn't grant the Ghost full cover, or any cover of any kind, but rather the ability to no longer be targeted.
However, Turn Undead, Dispel Evil and Good, Divine Sense and Detect Evil and Good DO NOT TARGET THE GHOST, nor do the latter effect the Ghost directly in any way, shape or form. And so therefor possession in not applicable as a defense against these spells and features.
Thus you can absolutely detect when a humanoid is possessed by a Ghost with Divine Sense.