Will deleting task in Smartsheet delete entered time from a resource's timesheet in Projector?

No. Once a Smartsheet task plan has been linked and sync'd with Projector, the tasks are truly tasks within Projector. Projector tasks with associated time entries or milestones cannot be deleted from Projector. In Smartsheet, you can delete these tasks, but following the next synchronization with Projector the protected Projector tasks will be recreated in Smartsheet under a row called "Deleted Tasks [date/time of sync]".