The Arduino ecosystem only provides a means of reading an analog input, on demand, it does not impose nor create any framework for the collection of data. You control when analog values are acquired and what is done with the resulting data. Data samples can be acquired in both time asynchronous and synchronous fashions, this behavior resides with your program design, not the Arduino hardware or software. You can queue data for later processing when the current program task finishes.
The big unknown is the time required by your non-data acquisition tasks - they must be able to process the data you've acquired before another dataset appears. Only when new arrives before old data is processed would there be potential data loss. As expected, you decide which data is discarded or ignored.