eAccelerator is a PHP accelerator & optimizer.
Its official web sites states that it increases the performance of PHP scripts by caching them in their compiled state.
They also say that eAccelerator should reduce server load and increase the speed of PHP code by 1-10 times.
Well, that's theory. In practice, frankly speaking, I couldn't tell the difference with or without it - on a few relatively busy php sites.
So - there will not be any problems apart from (potentially) slower operation of the php-driven sites.