Not at all, no.
Getting the unread count of PMs requires 3-4 database queries per AJAX call, where you do authentication and get the current user and then the unread PM count is basically free from that point in time.
Getting unread posts or replies... no. That requires at least another 2 queries per AJAX call, and they are expensive calls, not cheap ones like getting the user data. In fact, unread replies is the second most expensive subsystem in SMF, unread topics is third most expensive (search is the most), so doing that every 60 seconds would be an insane performance hit.
This is not theoretical, I have actually sat and implemented and benchmarked this stuff.