Are GPS coordinates more accurate if they are fetched at a small interval
Not really.

It's more accurate the more satellites it's receiving. On a shorter interval, it's most likely that more satellites are received, compared to just restarting every minute.

Also, it depends on your location. On a flat field, you will receive a lot of satellites fast, whereas close to buildings or houses, it will also take longer.

What I measured is that you could check the accuracy of the received location. If it's equal or less then 10m, the location could be used. If it's bigger, then wait until you receive a more accurate location.