As stated above yes all C code is valid in Objective-C since Objective-C is a superset of C. However this is a bit of a twist of words. The statement is actually
"All C Syntax is valid in Objective-C"
There is no guarantee that all your code will be 100% functional in an iOS environment. Since you can do things like make UNIX system calls from C or other machine/OS specific things there may be parts of the code that are not supported in iOS. If you wrote all the C code you are using and are sure that it contains no such calls or similar things than you should be fine.