No. That is not the advantage of open source. The advantage is that as long as somebody audits the code, you don't have to.
And in this case, you don't need to trust OWS to do the right thing, only to refrain from pushing rogue updates (ie, to only sign versions that are actual releases). You can still read the code yourself.
You've missed the subtleties around the word "trust" in the context. You don't need to trust that the WhatsApp people are nice, or want to do what is right.
You need to trust that they and Google haven't been legally compelled to push a "rouge" update - perhaps only to you. Don't forget there is nothing technically stopping a uniquely compiled update being pushed to a single account holder.
The only protection against this is 3rd party auditing and checking the signatures yourself, and that the 3rd party is completely located in a jurisdiction where they are unlikely to be legally compelled to comply with an order that applies to WhatsApp and/or Google.
WhatsApp supports an ungodly number of platforms. Probably they don't want to expose encryption in the UI until the feature/platform matrix is complete and there are no edge cases where traffic is unencrypted.
If you don't trust OWS to fail to publish malicious copies of its software, why would you trust them to fail to subtly sabotage their software?
I don't believe OWS would do this voluntarily, unless compelled by the government.
The situation is largely the same with Signal: Unless you manually build and install Signal yourself, there is no guarantee that the App Store or Play Store versions are actually built from the source provided by OpenWhisperSystems.
And even if you compile Signal yourself, there's always "Reflections on Trusting Trust".