Will voice activated control still work if I lose my WiFi connection?

No, the voice activated control functionality will not operate without WiFi. A notification of non-connectivity to the voice server will be provided in an audio response message. You must also remain connected to WiFi to receive automatic software product updates for voice control.
If your received WiFi signal strength is low on your thermostat, you may want to consider installing a WiFi range extender for your home. Honeywell has tested with, and recommends this model (Linksys N300 WiFi Range Extender).