Your sample code is showing some of the effects of pad temps (SVs_PADTMP flag). The first concat op ("begin". $count++) uses its private pad temporary to generate its result; the second concat just appends to this temp, which is then passed to save(). On subsequent calls, concat reuses the same pad temp, which is why setting it readonly makes your code die.
However, the \ operator has an explicit check that if the thing it's creating a reference to has the SVs_PADTMP flag set, then it makes a copy. Which is why your Data::Dumper output shows four separate values.