No, the Time Slider in ArcMap does not include the capability to detect when no data is present in a time interval.
In this context, no data present means the map does not display any data because no data falls in a particular time interval of the Time Slider.
The Time Slider provides visualization of temporal data over a specific time span, and throughout the entire time span, data may or may not be present at every interval. When a map is time-enabled to show changes of data over time, the Time Slider does not skip any intervals between the start time and end time when data is not present. This is by design.
The Time Slider is designed to work in a continuous sequence according to the time step interval set by users, and the option to only show time with associated data is not supported. The main idea behind the Time Slider is to represent data using a consecutive progression of time. Providing the option to ignore certain intervals of time because no data is present compromises the functionality of the Time Slider.
A workaround that allows only time with data to display when using the Time Slider is to adjust the time frame so that an entire year is condensed into a single day. However, this workaround may cause inaccuracies in date and time attributes for the data. This method is not recommended unless excluding time with no data is absolutely necessary when using the Time Slider.