Work is tricky because you have to carefully state the question. That is, you have to carefully state what is doing the work and what the work is being done on. I can think of three work questions here, the work done by the tension on the body, the work done by gravity on the body, the work done total on the body. Each of these has a different answer. (I could also consider the work done by the body rather than on the body) The total work done on the body will be zero if it ends with zero speed. This is because the work done by the tension on the body is the opposite of the work done by gravity on the body and the summation of these two is zero. If the body ends with some velocity then the work done by the tension was greater than the work done by gravity and we net non-zero work on the body.
If we ignore gravity and consider an object in space... Then the work done on the body will be positive. The tension force is applied over a distance and the object ends up in motion with kinetic energy. Then, if you pull the tension in the opposite direction of motion you will be doing negative work on the body (or the body will be doing positive work on you).
If I understand you correctly, yes, maybe... An object with buoyant force = opposite the weight of the mass (don't forget the opposite, we are dealing with vectors here) will be in equilibrium not traveling up or down. If you then pull on it with tension it will have a net force up resulting in a net motion up. But you also then get friction/compression forces acting against your pull because now the object is in motion relative to the fluid. Details can crop up in these non-ideal situations. So it depends on how hard you pull vs how viscous the fluid is. Pull too weak or have thick fluid and the fluid will rob you of kinetic energy and you will get no net work done on the object. Pull hard or have tenuous fluid then you will have kinetic energy in the end and net work will be done. In all cases work was done by the tension on the object. But it depends on the other forces whether or not net work was done on the object. (This is basically why we try to remember that newton's second law is a sum of all forces, not necessarily a lone force.)