Can you replace bottom bracket without removing chain or front derailleur? Can you service (i.e. fully remove and replace) a Square Taper English Threaded Bottom Bracket without removing the chain and/or front derailleur? Ditto for other BB types if the answer varies by BB type. 

Picturing it in my head, the drive side crank arm will take the chainrings and therefore chain with it as it is pulled, but the front derailleur wants to keep the chain where it is. If you manually pop the chain onto successively smaller rings, and then right off the smallest one as you pull the crank arm, then I think the chain will just hang off the derailleur, out of the way, giving you full access to the BB. 

Am I missing anything? 

Thanks.
Yes, it will come off okay.  There is no need to remove the chain or FD to access any format of BB.

You can either drop the chain off the Right side of the big chainring with your hands and let it hang from the FD to the lower wheel, or you can shift to the smallest chainring/granny and then lift the chain so it rests around the BB housing.

The FD has to clear the large chainring in its normal positions regardless of gear choice, so won't collide.

Either way will work fine, but you will get dirty.

Just try it, you're overthinking possible problems.



The real bear comes in trying to undo BB cups, especially if they've been on for a while.  Or you have weird left/right threads and not sure which way to turn it.  The right tools help hugely here.

The only thing I can think of in the way would be a chainguard.  They generally have to be completely unscrewed/bolted to access the chainrings.