The answer is no, it is not advisable to run new ECS software on the PC with older frame version firmware.  For example, if the frame is running ECS version 4.2 firmware then downloads to the frame with a PC running ECS 5.0 or ECS 5.1 should not be attempted as this will corrupt the configuration data in the processor cards on a Median or Omega size frame or the processor section on a E-Pico or E-32 frame. 
The configuration map size is dependant on ECS version and attempting to download the wrong size map into a frame will corrupt and possibly cause the processor card to go off-line.  If this happens the frame will stop working. 
To correct the issue the use of S4 driver software must be used to reload the processor card application firmware via serial com port using the ECS upgrade Reference Manual for the version of ECS software and firmware used together.
From ECS V5.0 and in later versions of ECS a map scheme was introduced so that if the frame received a configuration map from an incompatible ECS version it would reject the configuration map and report a "wrong map format" error message