Question: If the Universal Wave Function definitely existed, would that mean the Many-Worlds Interpretation was automatically true or would it only imply that?

Answer: 
Your intuition is correct: from the point of view of physics, there is no distinction between interaction and measurement. There is some argument about this, but as long as all interactions are accounted for, all the way to an observer's awareness of a measurement outcome, so that the observer is included as part of the system, then there is no distinction.

**But** that does not mean that all states are fixed. Let's say there are two particles, one of which is in a superposition of UP/DOWN states, and the other of which is in a fixed UP state. They interact in such a way that the second particle stays UP when the first particle is UP, and flips DOWN if the first particle is DOWN. The result is that the second particle, after the interaction, is in a superposition of states. In a sense, the superposed state of the first particle is transferred to the second particle.

Now let's complicate the scenario. Let the first particle instead interact with an instrument that measures its state. If the first particle is UP, the instrument panel displays "*UP*"; and if the first particle is DOWN, the instrument panel displays "*DOWN*". Now, after the measurement (remember, measurement = interaction), the instrument is in a superposition of states because the particle was in a superposition of states. BUT: the instrument has two "perspectives" corresponding to its two states: in the "*UP*" state, it "knows" that the particle was UP, and in the "*DOWN*" state it "knows" the particle was DOWN. The instrument *never* sees the particle as being in both states.

However, the instrument itself is in a mixed state. Now along comes an observer (who is just a really complicated instrument from the point of view of physics) who looks at the instrument and sees the instrument displaying either "*UP*" or "*DOWN*". The observer is put into a superposed state by looking at (interacting with) the instrument. The observer state that sees "*UP*" can only see "*UP*"; and the observer state that sees "*DOWN*" can only see "*DOWN*". The observer can never see the instrument displaying a mix of both.

This would all seem very abstract and unnecessary, except for the fact that it is supported by experiment. Young's double slit experiment, and other related experiments, demonstrate very solidly that a particle actually exists in a superposition of states until it is detected.

It's very difficult to design an experiment to prove that anything much larger than a small molecule can exist in a superposition of states, but [it has been done](https://www.nature.com/articles/news.2010.130). Proving that Schroedinger's cat - or a human observer - is in a mixed state may well be beyond our reach; but there is plenty of theoretical basis to assume that each quantum measurement puts the lab tech in a superposition of states.
Measurement is happening all the time *only* in the macroscopic world. The fundamental difference between a quantum particle and a macroscopic body is that a quantum particle is not interacting with its environment, or if it is interacting then it is not interacting in such a way as to generate the measured property you are interested in.

The conceptual difficulty in quantum mechanics is that in the absence of measured properties, particles do not behave in a way which we find intuitive. Indeed, one must go into the mathematical foundations, not just study the results, if one wants to understand it. I have sought to clarify this in a published paper [The Hilbert space of conditional clauses](https://arxiv.org/abs/1205.4607).