webMethods clustering provides failover support for
clients using Context and TContext classes. We are
using DSP pages to invoke IS services on integration
server.

Whether the %invoke% tag of DSP makes use of Context
classes or not? Ultimately, whether these DSP requests
support webMethods failover or not?

The %invoke% tag does not make use of the client Context class. Think of a DSP as a flow that provides control over the content of the response generated.

Once you have connected to the server, the duration of the processing occurs on that server. If the server crashes, the client will never get a response.

A load balancer of some kind is needed to front the cluster if you require fail over for DSP and service requests.