I don't own a scroll chuck yet, but I do drill on the lathe.
Not all the time but there are instances when It beats the drill press for a particular pen.
One of these is if I have a piece of antler that has an odd shape.
After turning it between centers I put a tenon on one end the size that will fit one of the Beall collets.(usually 3/4)
I put the Jacobs chuck in the tail stock as previously mentioned.
Doing it this way is slower but more accurate than readjusting teh DP (at least for me.
I can drill a longer hole fore a one piece pen.
( looking for longer bits)
This helps when doing long wood styles.
I uploaded a pen that used the method I described for drill anler that would be difficult on the DP,
It's in show off your pens and also in my album
http://www.penturners.org/forum/topic.asp?TOPIC_ID=7124