Well, it does make a difference. Without that line, this code throws an error, as expected. With that line, it doesn't. Seems like a potential bug.
The behavior is not unique to invalid subroutine calls. More or less any error under the (F) category in perldiag seems to produce this behavior - not all though, for example it still dies if I put in a division by zero. Though even then, it just prints the dying message - no mention of it having anything to do with BEGIN (unlike the other errors).
Update: above paragraph is slightly wrong. The difference has to do with whether the error can be caught at compile time or not. Compile time errors still die. But runtime errors get ignored in this construct.
Update 2: While re-reading perlmod I failed to notice the line chromatic quoted. So that at least explains why $@ and BEGIN have anything to do with each other at all. But I agree with demerphq; localizing $@ inside eval'd code shouldn't silently cause subsequent errors from that code not to be reported in the enclosing code.