I do not think there is an option to do that. Your best option might be to convert the files in smaller batches.
But since you want to update/convert them all, why you want to suspend that?
Thanks much. There is another tool that we have to run that will make use of the SolidWorks API and we do not want to affect the existing session. Hence I had posted this question.
As I understand, the TS would work in background and would open and close a new session for each file. This is expected behavior to avoid performance leakage after processing many files. So your other tool should not have any issues with TS unless they both are accessing same file at same time.
You can also cross check this via running both tools on small set of files.