De facto,
The source is your FCOM Chapter 15 Warning Systems.
The weather radar automatically begins scanning for windshear when:
• thrust levers set for takeoff
(....)
Alerts are available approximately 12 seconds after the weather radar begins scanning for windshear. Predictive windshear alerts can be enabled prior to takeoff by pushing the EFIS control panel WXR switch.
And to add to what latetonite already said:
Predictive Windshear Inhibits
During takeoff and landing, new predictive windshear caution alerts are inhibited between 80 knots and 400 feet RA, and new warning alerts between 100 knots and 50 feet RA.
Hence, without turning the WX radar on, you have no predictive windshear alerts for the first 12 seconds, and no predictive windshear alerts after 100 knots.
Basically you are taking off without predictive windshear at all with the radar turned off.