How much did you deposit? You really should do your research before using their service. Bitcoinfog is known on Reddit to selective scam. There's a short thread here, https://m.reddit.com/r/AgMarketplace/comments/3dqex2/bitcoin_fog_is_a_scam/.

You practically give them your bitcoin. You don't have access to it anymore. So in short, no. You can't get your coins back.

I haven't used that bitcoinfog but I heard bad news in the past for this (underground) website, were the stolen bitcoin from bter exchange send there? Few bitcoin mixing services that recently are still working are bitmixer and cryptomixer, both of them are good and still working, but first try to solve this issue with bitcoinfog, if the blockchain says that it is confirmed then its bitcoinfog responsibility to credit your account/address.