Mycelium is a phone only wallet. So if there is no wireless network, you can't use it. Blockchain is a web wallet, so you could use it on a computer if there is no wireless network and you get a wired network.
About the situation with "no network" connection but access to a wired connection, if you really need to you can export your private keys from you mycelium even when offline, so the funds are not completely unaccessible without wireless network.
Side note:
Having multiple wallets of different kinds is a must (imo).
Same as for fiat money, I do not know of anybody that has all the money located in one wallet all the time.
A typical scenario of everyday use is that you go travel, you take money from you safe, atm, etc. and put the money in your old school leather wallet.
I use mycelium on my android in a similar way, at home I use bitcoin-core, before I go travel I just transfer some funds to my android so I would be able to make transactions if I need to.
Completely agree with your side note. I use electrum on a usb bootable linux for coldstorage and blockchain.info as hot storage. I like mycelium, but i don't switch because of the bad wireless network i have at work.