Do people ever get a tooth abscess with no symptoms at all?

Yes: The nerve in the tooth can be dead, and you can have a lingering infection in the jawbone with little of no symptoms.

Not yet: By definition, abscess means swollen due to collection of pus in tissue. Tooth may not have symptom at the beginning after pulpal necrosis. However, as pus collected and put pressure on surrounding bone, pain occur if pus is not drain through a fistula or periodontal ligament space.

Absolutely: The vast majority of dental abscesses are not detected until they are advanced sufficiently to cause pain. Most fly under the radar, especially on teeth with previous root canal therapy. Swelling develops late in the process.