I think not, since, down to the millisecond, no two dates can be the same
You're assuming that when you get the time from your system clock that you have millisecond resolution. Even though you're getting a number of milliseconds, it does not mean that the hardware has a 1 millisecond resolution.
With most modern computers and operating systems, it's closer to 10 milliseconds. If you anticipate a high volume of calls, you certainly could read the time several milliseconds close together and they could get the same exact timestamp.
You'd be better off appending an auto-incrementing integer, or some random number or guid. If you wanted some sortability, you could add a timetamp and another number.
Also, you should keep in mind that the user can adjust the clock at any time, or it might change on its own if the system is synchronized by NTP.