Not necessarily. A full shock is usually noticeable and can feel like a sudden strong thump to the chest. Most people describe it as startling rather than painful, though experiences vary.
ATP (anti-tachycardia pacing), however, often works without the person being aware of it at all. It delivers a rapid burst of pacing to interrupt an arrhythmia before it escalates to the point where a shock is needed.
Some episodes of arrhythmia are also brief enough to resolve before the device needs to intervene at all, but the device will still record them. It is entirely possible to have a significant episode detected by your ICD without knowing anything about it until the data is downloaded at your clinic.