No! From the http://eaccelerator.net/ (my emphasis):
eAccelerator is a free open-source PHP
accelerator & optimizer. It increases
the performance of PHP scripts by
caching them in their compiled state,
so that the overhead of compiling is
almost completely eliminated. It also
optimizes scripts to speed up their
execution. ... eAccelerator stores
compiled PHP scripts in shared memory
and executes code directly from it.
eAccelerator only optimizes and caches your PHP files (thus eliminating most of the usual overhead when compiling static PHP files for each request). Dynamic data (e.g. DB, file system, remote ressources) are not cached (at least, not by eAccelerator). Therefore, your data will still be "fresh" from the requested ressource.
If, at a later point in time, you need to cache (some of) the real-time data (making them not entirely "real time") you could have a look at technologies like Memcached. This is specifically designed "... to reduce the number of times an external data source (such as a database or API) must be read."