Yes, you can game it even so, but it would be at least inconvenient for you.
Besides, if you do keep the stuff you don't want your client to see on another machine, then there's no reason to worry about being "spied" on. :)
It's been years since I've been an employee on any sites like that, but I still think the system is pretty bad. Just start with small projects and then scale up for high performing freelancers and don't offer repeat work to low performers.
Each snapshot is accompanied by a note of what you're working on as well (if you make one). If you're dealing with a client who'd question that, AND not accept/understand explanations, then you'd be dealing with many more problems from them as well, particularly without a work diary.