If the other person's privacy settings allow anyone to find them through their phone number, then they may see that you added their WhatsApp. If the privacy settings of the other party are stricter, and only the people they save as contacts can see their WhatsApp information, then they may not see your Friend Request until they also save you as a contact.
In short, adding a phone number of a WhatsApp friend does not always mean that the other party will see your WhatsApp information immediately, which depends on the privacy settings of the other party.