No, your number won't be visible to the person's WhatsApp unless he adds that phone number to his contact list. That's the way WhatsApp works and many applications of this type as well. WhatsApp scans the contact list of users and then displays the ones who use the service. Vibe, Snapchat, WeChat, LINE, etc work on the same principle, even if you have the possibility to manually add friends to your contact list.
