Honestly, no. Knit the entire bottom of the bag flat on your 24" circular, for the regular bag, 12"
circular for the Lunch Tote( I know the pattern calls it a lunch bag, I just like it calling it a Tote),
before joining it into the round.
Remember though, to leave a long enough tail to sew up the entire seam, maybe 24" to be on the safe side.
I like working the handles on two of the double points, but it really isn't necessary, it's just more comfortable for me.