The answer depends on what interpretation of quantum mechanics you subscribe to. Different interpretations have different definitions of 'measurement'.
In most of the 'wavefunction collapse' interpretations (Copenhagen interpretation), the answer is 'no'. An 'observation' requires some extra criterion to be met separating the quantum and classical domains - that the observer is 'big enough' in some way. Mass, spatial extent, number of internal states, the cumulative effects of some slight non-linearity in the equations exceeds some threshold, or (not scientifically favoured, but still popular) the consciousness or intelligence of the observer system. Proposals are speculative, and experimentally unobservable.
In the Everett (Many Worlds) interpretation, then yes, the interaction could potentially be considered to be a measurement. For example, (and oversimplifying the physics heavily,) the uniform motion of the centre of mass of the electron-proton system in a Hydrogen atom means their positions are correlated. Joint states in which the electron is offset one way have the proton offset the other way. The proton's offset from the centre of mass can be considered 'knowledge' of the electron's position. The atom remains in a superposition of states with the electron offset in every direction - from the outside point of view, the situation remains uncertain. But the proton's point of view may be broken down into a superposition of orthogonal (and hence mutually invisible and non-interacting) states, in each of which the proton 'observes' a different position of the electron.
If a wavefunction for a single particle is spread out over a region of space, then the different bits of the wavefunction do not interact with one another. They cannot 'see' one another. When an electron passes through both slits of the 'double slit' experiment, the electron passing through one slit does not 'see' itself passing through the other. There is, for example, no electromagnetic repulsion between the charges, affecting the interference pattern. This is a simple consequence of the linearity of the equations.
It is as if each possibility happened in its own separate world. The worlds can only interact with each other by interference, which manifests itself only in the apparent probability of events happening. Other interactions between different orthogonal parts of a wavefunction, like electrostatic repulsion, are forbidden. So it appears to each component as if all the other options have disappeared, and one outcome has been selected at random. However, all the options are still there, and to any outside system that is not correlated with the internal state of the atom (like us humans), the wavefunction still appears to be uncollapsed, as if no measurement had taken place.
The different interpretations of quantum mechanics all make exactly the same predictions about what we will observe in any given situation, and so are experimentally indistinguishable. It is therefore not a scientific question. The Everett interpretation has simpler rules (no mysterious collapse triggered by who knows what, or faster-than-light backwards-in-time paradoxes), but a far more complicated state (billions of unobservable alternate realities). Which picture you prefer is up to you. The idea of interactions and measurements being the same comes from the Everett interpretation and its close relatives. Collapse interpretations treat them as entirely different sorts of events, although they don't agree among themselves on what the distinction is.