Short answer: No.
To clarify, civilian alert burrows do not restrict movement either, all burrows do is to ensure the destination of a job is within the burrow (with massive cancellation spam as dorfs stupidly take illegitimate jobs only to drop them), but pathing has no interaction with burrows.
Also, the new needs activities frequently cause dorfs to defy burrow restriction (I haven't had any reason to get problems with civilian alerts, as all zones are within the burrow area, so I can't tell about that). You can burrow a dorf in his room and provide food and drink there, and still have the bugger socializing in the tavern (as all jobs are unavailable due to the burrow), run to the room, sleep, run back to socialize, go back to the room, eat,... I've also seen what I think is the jobs rewrite delayed job pickup misbehave, as I've had burrowed dorfs run to their burrow room, do stuff, and then run out with "no job", and then just stand there outside the room, as there's no activity to perform.
There have also been reports of civilians defying civilian alert burrows to wander about out into a siege without anyone understanding why that happened ("need to wander" satisfaction?).
In addition to bugs, you can easily screw things up yourself... One example is to have uneven terrain and mark everything that's below the ground level of your fortress entrance as part of the burrow, forgetting that you've got a corner of lower surface terrain with some logs that are eligible for hauling.