Yellow assert "Incomplete mesh data in Sprite. Please reimport or recreate the Sprite." spam in Console after loading/playing scene

1. From the Asset Store, download "RPG Map Editor" by Creative Spore
2. Assets > CreativeSpore > RpgMapEditor > Samples > Scenes
3. Load "demo1 - Big Map.unity"
4. Check Console. If spam does not occur, press Play

The "Incomplete mesh data in Sprite" warning will keep increasing until it reaches 999+.
"Reimport all" does not resolve this issue.

Occurring on: 2017.1.0b3, 5.6.0f3s2
Not occurring: 5.5.3p2, 5.5.3f1

---------------------------------
Old bug description
---------------------------------

1. Open attached project in 5.6.0b5
2. Open _OldProject > Scenes > MainMAin
3. Check Console

You will see hundreds of "Incomplete mesh data in Sprite" warnings.

4. Play scene

The number of warnings will increase to 999+.

Can repro on 5.6.0b5, 5.6.0b4
Cannot repro on 5.4.4f1, 5.5.1f1, 5.6.0b3s3

Might be related to https://fogbugz.unity3d.com/f/cases/873365/

Note:
On 5.6.0b3s3, this red assert is spammed instead:
Assertion failed on expression: 'spriteRenderingData->renderData->GetSubMeshes().size() == 1'
UnityEditor.DockArea:OnGUI()