Yes, but it depends on how you would like to handle escalations. There are three types of escalation methods available in osTicket: SLA's, transfers, and tasks.
An SLA will simply send an alert when the ticket becomes overdue.
Transfer is a manual method of escalation where an agent assigns the ticket to another agent, department, or team.
A task is when an agent creates a task within the same ticket, and assigns the task to another agent.