The limits placed on web services as far as frequency of running queued requests was set in order to reduce the performance impact on the system as a whole.
Web API calls being made outside of TeamDynamix have their own rate limits regarding the number of times a specific call can be made, but they will take effect immediately as long as the call is successful.
Even the old SOAP Services (which you could use, but you'd have to hard code everything into your call including the authentication portion) were limited by that 15 minute timer. They didn't allow for getting around that timer.
If you have any other questions about web services or the Web API, please let me know and I'll be happy to help.