To understand numbers on specific hardware, I have in the past started Tomcat bare (not even the manager app), and then Tomcat with my specific web app. The startup time has indeed been in the milliseconds ( I happen to embed Tomcat in products so I have had to understand such things).
In my use cases, startup time has been of less importance than execution time, the JIT pause, and the GC pauses. So I tend to run the jvm is server mode.