Absolutely they are often taken before you get the email. Many times there will be a delay of up to several hours between the time I take a job off the company's job board and receiving notice that it is available. Whether this is an email issue on their end or mine I have not investigated. Also there is inevitably somebody with a faster internet service or who is actually on the site when the jobs are posted who is likely to pick up stuff that you might be interested in. And then there are the emails for the 'dog' shops that nobody wants because the pay is not commensurate with the requirements. Then there are the companies that I suspect send out their emails in multiple waves--the first to their regular shoppers and the later ones out to everyone--because I get the email an hour or two before some shopper friends do.
Part of the 'art' of being a mystery shopper is figuring out when shops are most likely to be posted and be checking the job board regularly during that time frame. Sometimes a friendly scheduler will tell you that they plan to post shops on a specific day, sometimes they will indicate a two day time frame such as, "If you don't see them Wednesday, they should be going up Thursday morning." One of my most productive companies posts on a particular day of the week between 4PM and 6PM but most frequently between 4:30-5:00 PM. I am there, like a vulture, waiting to swoop down on the shops. An hour after they post they are all gone and trust me, I did not take them all!
One suggestion is to develop friendships with other folks on the forum who are in areas near but not on top of your shopping area. Generally they will be seeing and doing the same shops you are doing. Develop the relationship through PMs and when you figure they are trustworthy not to include you in forwarding 'cute stuff' with their hundred other closest friends (the address lists that accumulate with those seemingly innocuous joke and inspirational messages are harvested by spammers), exchange work email addresses. Direct email is a whole lot faster than PMs. When you see jobs just posted, drop the group a quick email and encourage them to reciprocate. But directly checking the boards and figuring out when companies post is your best defense for finding the jobs.