No, you do not need to connect your Laser Egg to Wi-Fi in order to monitor you air.
However, connecting your Laser Egg to Wi-Fi allows you to control it from your phone, change settings remotely, and access certain features, such as:
- Display readings in different Air Quality Indexes (US, China, or India)
- Display temperature in Celsius or Fahrenheit
- Fetch and display local weather forecasts
- Connect to Apple HomeKit
- Connect to IFTTT