Technically, no, it's not safe, moreover, anyone else on the server can read your files/passwords and so on if they're not properly chmoded, if you do not have shell access to your host, then your host is lame.
PHP's safe mode is a terrible hack that can't really get around this problem, unless you really cripple your php and destory what makes unix so powerful. (for example, safemode alone means crap, if popen is enabled.. or any of the exec/system calls......). PHP's mode is a hack for a problem PHP developers shouldn't have even tried to solve.
This problem will be TRULLY soved by apache 2.0 and it's perchild mpm, as that will finally allow apache to make file system requests with a proper uid/gid of the virtual host owner.
There is really no easy solution with apache 1.3+PHP to this problem. All of the attempted ones are terrible crippling hacks. Apache 2 is the answer.