In summary: Difficult to tell. Google is very late to the party. Reason: Facebook, Inc. owns the chat market. In this article by the Verge “
Why Google's Allo messaging app is a big step backwards”, they argue that Google’s Allo is a big step backward. In short, one needs to realize how enormous Whatsapp and Messenger are:

Facebook has 1 Billion monthly unique people using Whatsapp and 900 Million unique using Messenger. Competing with that is extremely challenging.
Google attempted to market many chat/communication like:
Google Talk
Buzz
Hangouts
All were not as viral as Messenger or Whatsapp. Now, google’s card is an Artificially Intelligent chat app: Google’s Allo - something new. However, that doesn’t guarantee winning over Whatsapp or Messenger because:
Practicality versus CreativityThink about the Google Glass. Everyone was excited about it, within saying “Okay Glass, take a picture”, the Glass would take a picture along with other features.


However, Glass failed. Not because it didn’t have good technology but because people didn’t find it practical: while work, while driving, while biking, etc…
See:
Why Google Glass Failed And Why Apple Watch Could TooThe same could be with Google’s Allo. Think of what it can do:
If a person, sends you a picture of a butterfly, Google’s Allo will send you suggestions on what to say to this image. There is a big amount of artificial intelligence implemented. But will you really find that practical when friends send you a picture?
If you mention the name of a restaurant. Google can reserve a restaurant near you by just asking the app to do that. Will you find that practical or you’d prefer to call the restaurant yourself?
Similarly, you can send emoticons by specifying their size. But will people really find that magic and switch from Whatsapp?
You can ink photos (draw on them) while sending them. Google will suggest smart replied too.
And so on…
Google is on the bottom of the competition, they have many disadvantages too: Messenger App: It is integrated with Facebook. We, consumers, love to chat directly with our friends from Facebook. That is a big disadvantage for Google. If you’re planning going out with a friend, will Google’s Allo be this advantageous that you would switch to that app?
Whatsapp: I’m pretty sure that Facebook has a well-trained marketing team, whose job all day is would be to monitor Google’s Allo progress and implement all the features which find useful for it. At the end, they’re in the 1B club.
Privacy still remains a major concern with Google as in the past, it's most prominently used Gmail app was found guilty of breaching user privacy. However, Google claims that Allo is encrypted end-to-end and Google will not be saving any data created by the app on its servers.
While Google might claim so, we think otherwise. This is due to the fact that it has theGoogle Assitant baked in, which not only analyses the chat to give you better chat responses but even suggest places based on the conversations.
More importantly, it learns over time. This means that the app will be throwing chat data back to Google servers and then giving you the suitable responses.
That said, there is an incognito mode in the Allo app, borrowed from the Chrome browser, which bypasses the Google assistant and encrypts the conversation between users. However, users will not be able to take advantage of the Google Assistant, while chatting through the incognito mode.
It seems like all you have to pay for privacy is some inconvenience. This could be a big challenge for Google to bypass WhatsApp and take over more users.
In summary, it is not guaranteed that Allo would be extremely successful and come close to Whatsapp or Messenger. Google tried to force Google+ from YouTube in the past (and still do) but today you can clearly see that it is just not that successful.