At a particular time, when an analyse is run on a database, we are uploading a bulk data from excel sheet. Will the analyse slows down the writes performed at that time?
I don't think it will considerably slow down bulk uploads. Analyze reads sample data from the table being analyzed to build statistics for planner to use. So there is definitely some read IO that will occur. But the extent of the reads will depend on the size of the table and statistics gathering settings.
AFAIK overhead of analyze can also be controlled by appropriate settings of vacuum cost parameter.