Yes, you could do this, but the short duration static file that typically results from this method will result in post processed accuracy of > than 2m or more which stops it being useful.
Stop and Go files are a single static file that has markers in it to identify when you stopped for a short time.
The post processing software has sufficient data in the file to work out the errors properly. When it processes the marked points it is just computing a position and applying the error corrections calculated on the whole of the data in the file.
regards Bryan