Can a RapidConnect device handle multiple simultaneous requests over serial?

In short, yes. Multiple commands can be issued over serial and the module will respond with a serial frame to the Host for each individual request as it receives a response over-the-air. Each response will contain a transaction number corresponding to the request, so that you know which request it belongs to. Note, 'out-of-order' command handling may make the implementation more complicated. 

The application support message queues for all incoming and outgoing network commands (ZCL and ZDO), with a maximum of five incoming and five outgoing messages at a time. Messages are retained in the queue until they're acknowledged appropriately, after which they're cleared out to make room for the next message.