Counting on one is a sure way to lose everything, maybe not this time, but sometime.
True, true, true. And on a second-hand drive with possibly unknown history and operability to boot. Prudent retentive types also spool off DVDs of precious files from time to time, even in a multiple drive scenario.
There is an online backup company
that offers 2GB of free storage, definitely worth a look, but they could go belly-up (gotta look at all angles, don't want to add to Ed's mildewed shoulder)
But, to answer the question, yes, you could leave the drive connected, but why? When it is so easy to remove and add back, it makes sense to play it safe and remove any extraneous drives while formatting, especially precious ones. If it's connected via USB remember to use the "Safely Remove Hardware" feature in your systray to stop the drive before removal. Now you have ZERO chance of making a mistake or having Windows write something to the drive during OS install. If your OS is the same, the drive will be recognized after you reconnect it. ALL of us have formatted the wrong drive at one time or other...
I would highly recommend buying a stack of DVDs, though, and spooling off all of drive 2's data first and foremost. Buy quality media (Fuji, Memorex, Maxell, Sony) too, it's only a few cents more per disc than house brand. If you don't have a DVD burner they run about $40 or less these days. Best of luck!
Tony
"Buy what you like, or you'll be forced to like what you buy"...me