[Hampshire] tail -f logfile in screen session ... server die…

I am just wondering ( the way you do when you do something
out-of-the-ordinary and something else odd happens...)

yesterday I tried setting up a 'screen' session on a remote server for
the first time. I am not a screen user but have had it recommended to
me by various people. One of the virtual terminals in the screen
session was doing a tail -f of a log file, as I recall.

This morning the server was deadly slow and unresponsive - not quite
dead but bogged down. Am getting the data centre to reboot it as I
write. That screen session would not lead to a huge memory footprint
... would it??