What I have been wondering is whether an earthquake can affect a closed system survey. We are using Leica TCR 307s and TCR 407s and I was wondering if an earthquake can throw off your fixed points if staying within a 500m grid? The fault line does not run through the site.
I think it can, if the earthquake in question induces substantial tectonic movements. There has been a study by IIT Bombay, India where the researchers have found out that their fixed positions have moved as much as an inch over a long period of time (7-8 years).
If your survey is short-lived i.e. you are not fixing the total stations for a some future readings, I don't think it should be a cause of concern, as you said the fault line does not pass through the area.
You are effectively asking if the relative positions within a 0.5 km x 0.5 km region would have distorted? In my opinion that is more of a geotechnical question. It also depends if the maximum distortion change from the earthquake is greater than the instrument measurement error from the total station.
Generally, if the site is on hard bedrock, there shouldn't be much or any relative changes, as the whole site would move (each point should be relative to each other). But you could expect some distortion on a soil with "plastic" characteristics (e.g., plastic clay; see Compressability), or if you have unconsolidated sediments and a shallow water table (see Liquefaction/Soil liquefaction).
The best way to find out is if you have any "known" locations, resurvey these and check to see if the relative distances have changed between them before and after the earthquake.