Help from Prosecutors, Detectives, Coroners...

Just guessing here (educated guess, but still a guess) but yes, they would remove everything in the storage unit and process it for evidence. If nothing was found on most items, they would release it to the owner (provided he was cleared as the killer) fairly quickly.

Depending on the size of the facility, I would doubt it would be shut down completely while they processed the scene. But they would keep everyone well back from the scene. Most of our storage units around here are laid out in rows. If that's the case, I would guess they would shut down that the row the unit was in.

I once had a call involving a 2 month old body in a VW, inside a storage unit of a large facility. (I later used it in a novel) Kristie's "guess" is pretty right on, except that ours was in the middle of the night, so we didn't have to shut down anything and the row was available in the morning.

After some investigation it became clear it was clearly a suicide, however, not a homicide, and that probably made a difference.

To be sure you can call your local police dept homocide unit or detective unit and/or the local/regional coroners office.

...or just the motorcycle in which the body was found stuffed into the saddlebags and trunk?

These had better be jumbo-sized or else have a very small body. Adult limb/body average; 12-16" fore/upper arm length, legs upper/lower: 16-20", head+neck: 14-18: high, torso 22-30".