It is pretty standard practice now for desktop applications to be self-updating. On the Mac, every non-Apple program that uses Sparkle in my book is an instant win. For Wind
Yes it would be a security feature if PHP went and overwrote its files from some place on the internet with no warning. There's no guarantee that the server is connecting correctly to your update server (it might download someone code crafted by someone else if DNS poisoning occured) - giving someone else access to your client's data. Therefore digital signing would be important.
The user could control updates by setting permissions on the web directory so that PHP only has read access to the files - this procedure could simply be documented with your program.
One question remains (I really don't know the answer to): can PHP overwrite files if it's currently using them (e.g. if the update.php file itself needed to be updated)? Worth testing.