Is it possible to have a stored procedure or set of SQL code run periodically by specifying a time-based trigger in SQL Server?
Not directly, but look at SQL Jobs.
A job is a specified series of operations performed sequentially by SQL Server Agent. A job can perform a wide range of activities, including running Transact-SQL scripts, command-line applications, Microsoft ActiveX scripts, Integration Services packages, Analysis Services commands and queries, or Replication tasks. Jobs can run repetitive tasks or those that can be scheduled, and they can automatically notify users of job status by generating alerts, thereby greatly simplifying SQL Server administration.
(emphasis mine)
You can use a SQL Agent job. IF you have a requirement to run on Express editions, that lack SQL Agent, you can use dialog timers and activation.
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