The simple answer is NO.
Instead, the app is linked to your existing phone number.
When thats done, you might send them a message.
you could also make voice and video calls without having to use your minutes.
This will consume your data allowance at a fairly slow rate unless you are connected to a Wi-Fi hotspot.
A quick summary: No, WhatsApp does not give you a new phone number.
Its tied to an existing one and uses data services for send messages and make calls.