Installing a SSD, should I or should I not disconnect the battery (MacBook Pro)?
You don't need to disconnect the battery, but it's a good idea.

The only reason you disconnect they battery is to ensure that there is no power on any of the circuits which could inadvertently be shorted.

If people fry their logic board while disconnecting the battery, it's most likely they used a metallic tool (like a screw driver) to pry up the battery connector; use a plastic spudger tool.