Or, you could just import the BIP39 seed onto any supporting desktop wallet clients. For instance, copay. Though instead of "import from backup" you'd have to go to create a new wallet, and specify the recovery seed.

i have tried this before, generate a new wallet on blockchain.info, write down the walet recovery seed, and if you ever lose access to your wallet then you could either do it the hard way, go through all the derivation paths etc. or just import it into any supporting bitcoin wallet.

So yes, you can indeed access your coin without having access to the site, as long as you have the correct recovery seed.