I think you're asking, "If we know an object's shape, can we determine if it is in in hydrostatic equilibrium?" If so, one might wonder if astronomers classify basketballs or ball bearings as being in hydrostatic equilibrium, since they're so spherical.
Below about 100 km in radius, the answer is in general no. Given some population of randomly lumpy objects (like asteroids), some of them will be close to the shape of a sphere purely on accident. The composition matters too -- an object of this size made of hydrogen gas would assume a spherical shape from hydrostatic equilibrium, but an object made of rock might not (like Mathilde below). We could make better predictions given detailed knowledge of the materials and environment of the object, but this is not always possible, as you mentioned. For small objects, intermolecular and atomic forces dominate gravity.
Once you get to a certain size of object, it becomes much easier to make a prediction about hydrostatic equilibrium. This is still very much context-dependent, and you still get complications from material composition, temperature, etc. However, atomic binding forces have some fixed strength, but gravity scales like mass. Given ordinary astrophysical materials, we can be very sure that a body like Jupiter is under hydrostatic equilibrium.
You can make some order of magnitude estimates by assuming that the atomic interaction energy must be at least as large as the thermal energy (Hughes and Cole 1995). If you check out equation 5 of that paper, you'll see an explicit expression for a radius that divides spherical objects and nonspherical ones. At some mass, the binding atomic energy becomes dwarfed by the gravitational potential, and you always get a spherical object.
tl;dr -- small objects no, big objects yes, medium objects may require detailed modeling.
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