Does Reaper contest the point in his Wraith-form?

Yes, but with a caveat.

Reaper (and Mei, to cover both immunities) can both contest points or payloads owned by the enemy. This is easily seen in most games, so I don't feel proof is necessary.

The caveat here, is that they cannot capture points. I did not test payloads, but I can safely assume the same logic is behind it.

Reaper using Wraith form on an unconstested (neutral) point.

Mei using Ice Block on an uncontested (neutral) point.

If necessary, I can also knock up some video evidence of trying to capture an enemy point while not contested, but I don't think there will be a difference.

==EDIT==

As per Blue-Raja's comment, I did further testing on the nature of Overtime and contesting versus capping. My results were fully in-line with the above evidence- both can contest a point and extend Overtime during the duration of their in-vulnerabilities, but neither can capture a point or move a cart in that time.

While not appearing to be the greatest of sources, it does appear that Reaper can contest points while in Wraith Form. It is not clear if he can capture points while using this ability, but I believe he can still move payloads while in Wraith Form.

As far as I can tell from sources and experience with the game, Mei can also contest a point while in her invulnerable Ice Form as well.