My initial gut reaction is to say yes, however, I'll wait for the experts.
From Rule 5 (http://www.dixie.org/Uploads/Dixie/NATSB/HTMLPages/rule5.asp)
NOTES ON THE ABOVE: The responsibility is now completely on the baserunner. There is NO obligation on the pitcher to LOOK, FAKE or THROW.
A base on balls or dropped third (3rd) strike in which the
batter is entitled to run, is treated the same as a batted ball.
The batter/baserunner may continue past first base and is entitled to run toward second base, as long as she does not stop at first base. If she stops AFTER she rounds first base she then must comply with Rule 5:01 (B).
From rule 8:
http://www.dixie.org/Uploads/Dixie/N...ages/rule8.asp
NOTE: In the DIXIE DARLINGS and ANGELS divisions the batter that receives a base on balls must stop at first base. All other baserunners may advance only if they are forced to do so.
I see this as a yes to your question, only Darlings and Angels are restricted from advancing.