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Not exactly, but you can make something work.
You can run macro's at startup and shutdown, which could set a bit in your PLC to indicate as such. In the event that the screen loses power without going through a proper shutdown procedure, this won't work of course, so it depends on the details of what you're trying to detect and why.
A more reliable, but slightly more complex option is to create a macro which is event triggered. Tie the event trigger to the system/seconds or system/minutes HMI tag, so it triggers the macro every second/minute. Inside that macro, set a bit in the PLC to 1.
Assuming you use the seconds tag, the bit in the PLC wil be set every second. Run a timer in the PLC unconditionally, and every time the bit gets set to 1, set it back to zero and reset the timer. If the timer ever reaches, say, 4-5 seconds, your HMI has stopped.