Is it possible to rebuild index of oracle 11g table while keeping the application running and access/update the table?

yes you can rebuild index online 

It will affect only the efficiency during the implementation process

After that everything returns to normal

yes, rebuild the index online.

alter index <index_name> rebuild online;  is the query to rebuild indexes while users are accessing data in table.

Yes you could do that rebuild the index online and everything will be normal in the process if you have oracle background.

When you use an online index rebuild Oracle has to create a log of all changes you make to the table while the rebuild is running. Once the log is set up, Oracle creates a new index using a read-consistent copy of the data in the table, then copies the logged changes into this index, and finishes off by tidying up the data dictionary, dropping temporary segments, and dropping the log.

http://jonathanlewis.wordpress.com/2009/06/05/online-rebuild/