In short, no. You need root access to install the accelerator - however, it's certainly possible to have an accelerator such as APC disabled by default then enabled on a virtual host, or folder basis using the apache configuration. if you have a friendly admin they may be willing to consider implimenting since it shouldn't interfere with other sites (this is what we do for our customers with ez sites), e.g...
#
# APC disabled by default
#
php_admin_value apc.enabled 0
#
# APC enabled for ezpublish
#
<Directory /usr/local/share/ez>
AllowOverride All
php_admin_value apc.enabled 1
</Directory>
