There's no reason why you can't replace an SSA cache battery while the
system is running, other than that it would be practically impossible due to the physcial limitation of the design and one's fingers etc.

The battery is a standard AAA rechargeable tripple battery wrap, with a non-standard two pin clip on it - in that it doesn't match any of the commonly available in the shops varieties. 

However, one can and I recently did, go buy a common or garden such battery, chop off the wires about half way and solder on the equivalently cut original clip and remaining wires from the official IBM part, covering exposed leads with shink-wrap tubing. 

Once you get access to the place where it clips in - covered by a spring steel section - you can simply plug in the new battery. 

I had to unscrew the cache card from the main card to get that access comfortably, so you won't be doing that with the system on of course.

Having said that, there's probably not going to be a problem if the battery isn't in the steel holder or even on the card - it could hang there somewhere and thereby you could perhaps get to the clip alone with the system up.  It would be devilishly fiddly !