Not sure what state you are referring to, but in most states, TAW will not delay any comp or save any UPS numbers. Usually someone on TAW can draw partial comp instead of full comp, so there really is no financial advantage.
If someone needs to go out of work totally, then it does cost some more (in real comp and UPS numbers).
But let's be honest here, if one can do some tasks if injured on the job, and the problem appears to be a short term problem (30 work days), why would one not want to work TAW???? It keeps the benefits active and provides income to the injured worker while waiting for partial wage loss benefits to kick in....the union still gets their union dues....the employee does not feel the need to burn any sick/personal days while waiting...the employee does not get used to watching the Flinstones while those that took the caution not to get hurt, slave all day.....
If it is obvious the problem is not expected to be resolved in the next 30 work days (6 weeks) and if the tasks that the employee is expected to perform are not that needed, then yes, perhaps the employee should be out totally and the TAW days should be saved for the tail end....one call to the Labor Manager in the district should resolve this.