Yes, it is useful to know some general topology to make any headway in commutative algebra. A very powerful technique in commutative algebra is that of completion of a local ring. Such complete rings are often easier to deal with and geometrically they contain important local information.
The process of completion actually borrows amply from general topology. Also topology is the first instance where you start worrying about important properties like compactness, separatedness, properness etc. It will be very difficult to understand the application of some concepts of commutative algebra (in algebraic geometry I guess) without topology.