No, there is a minimum. The content has to remain down for at least 10 business days AFTER the counter is received by the hosting provider, to give time for the purported copyright owner to go get an injunction or other relief.
(The counter also requires disclosure of intensive amounts of personal data, which the initial notification does not, but that's probably the smallest problem with the DMCA system.)
Ah! The times when it's gotten restored immediately involved a change in hosting or pointing out defects in the original notice, or the hosting provider accepting liability because the counter seemed sufficiently strong to take a stand. I didn't remember there was an actual 10-14 day lag written into the law.
(Thankfully, I've never been the one to actually handle DMCA issues from the service provider side myself.)
(The counter also requires disclosure of intensive amounts of personal data, which the initial notification does not, but that's probably the smallest problem with the DMCA system.)
See 512(g)(2) B and C of the DMCA for cites.