You'll have to loop through the segment collection of each feature's geometry. Use TypeOf (VB.NET) or Is (C#) to see if a segment implements one of the interfaces associated with curves (i.e. ICircularArc, IEllipticArc, etc). Unless they've added some new types recently, pretty much anything that isn't a Line is a curve of some type. So, you could just test the segment to see if it isn't ILine.
Would the ITopologicalOperater isSimple() give you the same result?
Not really in this case. isSimple will just tell you if a geometry is topological correct regardless of the geometry type, whereas the original question was more about 'does my feature have any curves in it.