would this be enough to create an viable atmosphere or should a dome be put over it?
If you want to create an atmospheric pressure that humans could survive without a suit, the dry ice in the polar regions is more than enough, the trick with Mars is raising the average temperature 5C at which point you'd create a runaway greenhouse.
As for just water needs, the polar regions are lousy with water ice (the northern cap alone has more than 800k cubic kilometers of water ice and a cubic meter of ice is about 917L so yeah, a LOT of water). There's also suspected to be considerable amounts in the regolith all around the planet and given there might be this underground lake there could possibly be many more.
It does offer some radiation protection too but it would take centuries with current technological means to raise the temperature enough on Mars to start a runaway greenhouse effect... as it stands now you'd basically have to go set up power plants on Mars then start producing greenhouse gasses from local materials, releasing them into the atmosphere, until you got that estimated 5C average temperature increase which would then start melting the polar caps' dry ice and water ice (as well as what is in the regolith all over the planet) and go runaway. At that point you'd be outpacing what the solar winds are peeling off the atmosphere (IIRC it's something like 100 grams a second which sounds like a lot but not on a planetary scale).
The very thin atmosphere it has now, will take another 2 billion years or so to be stripped away entirely.