The question isn't valid because domains only matter when describing or manipulating the data using dimensions in $n$D space. They are a way we conceptualize numbers in relation to each other, not anything intrinsic about those numbers themselves. The File Sink takes the complex data on its input and writes it out to a file as binary values in the described manner. The idea is that the File Sink saves the data such that something else that does care about the domain(s) can manipulate or present the data in a particular domain. If you are familiar with the software practice of serialization (or pickling) it wouldn't be completely incorrect to think of the process in those terms.
"Sample Rate" means something related but a little different when considering Sources and Sinks. Sinks often behave as if they use the sample rate to determine the actual values for incoming data. Think of the sample rate as a "ruler" that the Sink needs to use to measure what the actual values of sample-dependent data of the incoming data are.
You can try this yourself. See what a GUI Sink displays for the actual value of the frequency components when you set its Sample Rate setting to
samp_rate/10. The results will look the same, but the actual values reported will be scaled down by the amount you have chosen. How this affects the File Sink is left as an exercise for the reader, but my guess is that the values it saves will be scaled down by any "under-sampling" factor.
(At the risk of introducing link-rot, you should definitely watch Michael Ossmann's Part 4 presentation on sampling in GNU Radio. Actually, watch the whole thing, and do the "homework". Seeing someone describe it and then trying it yourself answers these questions better than I could.)
A comment has pointed out that one could think of the saved data as in the time domain under some circumstances because it is literally series of 32-bit values written as fast as possible in time order. I think this is a conceptual mistake, however. It only really holds for data that you know is sensible values vs. time. But since any data could be read into it then you would already know this.
So, yes. If you are capturing Complex data, it will be a series of real and imaginary parts in order that could be easily expressed as being in the time domain. It still needs to be interpreted by something. Whether that interpretation is a YT graph or an FFT, it is still interpretation.