If a site or tool like multisig ever goes away or offline, I can still access the wallet, no adverse affect, correct ?
Ummm, depends. Multisig in and of itself is 100% on the blockchain, so:
1 multisig address = X standard addresses + # of signatures required.
That's it. When money is sent to that multisig address, in order to send it out, you need the necessary # of signatures, or else the blockchain will reject it. And the only private keys that can sign the outgoing transaction are the "X standard addresses" the multisig address was created using.
For example, if you're using a multisig service that's a 2 of 2 solution (1 = you, 1 = the site), and the site disappears, then your funds will be stuck. You need the private key from the site to send any funds.