When uploading a world so people can download it, will entities be in the same spot?

Short Answer: Yes, the entities will still be in the same spot.

Long Answer:

When a client world is paused or closed, the world is unloaded and saved. When chunks unload, the writeToNBT method of all entities within the unloading chunk will be invoked causing the entities to write their NBT tags into the chunk's save file in the world save file.

With help from MCP and Minecraft wiki, all entities have a Pos tag which consists of 3 Double_Tags which respectively stores the xyz coordinates of the entity.

Apart from the Pos tag compound, many other tags and tag compounds are stored for each entity, some are entity type specific such as Size for Slimes and Magma Cubes and Fuse for PrimedTnt.

So when the save is uploaded, the level.dat file is within the uploaded file, thus when the client reloads the world, or more specifically the chunk the entity resides in, the entity's xyz coordinates and all other NBT tags will reloaded as the method readFromNBT is invoked, so all entities will be in the same spot the world was last saved.

This is may not be the case if there was errors when the world is saved causing the world to corrupt and may turn into "read only" chunks in which no blocks or entities can be saved.

Yes, they should. All world data is stored in the world file, including entity locations.