No.
Exporting your data will not remove any information from the online surveys system, nor will it interrupt the running of your survey or close your survey.
Exporting your results generates a copy of the information held on the online surveys servers and converts it into the format that you have chosen. The original information is retained within online surveys.
You can export your data as many times as you like, and you can do this at any time, whether your survey is open or closed.