I finally found a way.

As it turns out, since what I really want to do is check for link, I don't need ifup at all. Instead, I can use ethtool (though it has to be installed first), like so:

connected=$(ethtool eth0 | awk '/Link detected:/ { print $3 }')

If, however, I did need to check ifup, I could use a background process and the $! shell variable. If I just wanted to check whether it was still running after the timeout, I could do this:

ifup eth0 &

sleep 5

if ps -p $! | grep -q "$!"; then

    connected='no'

    kill $!

else

    connected='yes'

fi

If I wanted to capture the output from ifup, my best bet would probably be to redirect it to a temporary file. (I looked into named pipes, but I don't think they'd work for this purpose; ifup would block until another process was reading its output.)