You are correct in saying that you have to run the profiler while you take the snapshots. You might be able to reduce the profiler's overhead slightly by turning off the 'monitor disposal of objects' option while profiling, however, and by recording as few performance counters as possible.
On your other question, you can take the snapshots and then analyze the data later. When you have finished profiling your application, in ANTS Memory Profiler, go to the File menu and click Save Profiler Results... You can then use the Open Profiler Results... menu option to open the results later, when your application is not running.
Hope that helps,
Red Gate Software.