The Timesheet Adapter is really great for populating your CA PPM timesheet with information from another system(s). It does not submit or approve the timesheet, that would need to be done by the resource and resource manager. The one limitation of the adapter that I am aware is the adapter will not create adjustment timesheets.
If time will be adjusted in ServiceNow after it is sent to CA PPM and/or timesheets are submitted/reviewed/approved in ServiceNow, then you should look at using the Transaction Adapter for CA PPM. The actual hours will be capture in CA PPM, along with adjustments, for all investments, but there are no timesheets to submit, review, approve, post, or adjust. This does leverage the financial processing, so basic financials would need to be setup in CA PPM.