Can you replace bottom bracket without removing chain or front derailleur?
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.