Yes, they do!
It's not proof, because code which happens to work without race condition does not proof, that there is no race condition.
The *ONLY REASON* print and readline are said to "not work with select", is because they will block if they receive a partial message, thus preventing the code from getting back to the select
You don't give proof for that.
Now my proof is select man page and this:
For efficiency, Perl uses a trick called buffering. The first time you ask to read from the file, Perl has to make a system call. Since system calls are expensive, it plans ahead. If you tried to read a little bit of text, you will probably want to read the rest later. The blocks on your disk are probably about 8K bytes, and your computer hardware is probably designed to transfer an entire block of data from the disk at once. So instead of asking the system for a little bit of text, Perl actually asks the system for an entire blockful, which hardly takes longer to get than a little bit would have. Then it stores this block of data in a region of memory that is called a buffer, and gives you back the one line you asked for. The next time you ask for a line, Perl already has the line you want in memory in the 8K buffer. It doesn't have to make another system call; it just gives you the next line out of the buffer. Eventually you read up to the end of the buffer, and then Perl makes another system call to get another bufferful of data.
You can see this when executing eof() of FH with data and running select then. Select won't return "can read", while there was data in FH. But readline will return this data. That's because readline reads not only from file, but from buffer as well.