Yes, all true, to an extent. You can typically can buy them at your local grocery store (somewhere out in middle Oklahoma, probably not ), and they will typically survive for a ranging amount of time. At the grocery store, you'll buy them as either littlenecks or cherrystone clams. Same clam, different name to indicate a size difference. For coldwater, it depends. Mercenaria mercenaria, the clam you purchase, has a massive range. All the way from the St. Lawrence gulf, above Nova Scotia, down to the Florida keys, and in the Gulf of Mexico.
The ones at the grocery store are typically farmed raised in Florida, so I'd imagine they are somewhat warmer then chilly Canadian waters. However their 'optimum' temperature I found online was 20°C, or 68°F. Well colder then our typical reef tank. But I think it's the distribution process, of them being shipping dry, on ice, and sitting at the supermarket on ice all day and night, that plays a majority role in their low survival numbers.
My personal experiences has been just a few will live for any amount of time. I do have some that are still alive, years after I bought them from Publix. Most die in a few days. I buy them for food for my fish anyways, so no real loss. There really isn't a disease concern, they've been out of the water long enough. They do still need flushed first. Put them in a bowl with tank water, and they will siphon in fresh tank water, and expel all the crap they've been holding in. They usually 'spit' when they do this.
For a source of nitrate reduction, actually all clams, crocea's, maximas, etc consume nitrates. However their levels of consumption are on the same timeline as mangroves or even xenia. They aren't very quick at it, and commonly available and hardier macroalgaes do the job better.