Selecting the expand_rootfs option only modifies the partition table and then says "The filesystem will be enlarged upon the next reboot". That process on reboot happens before sshd is started, and it can take many minutes on a large card.
So, resizing does not stop sshd from working, but it does delay its next start. It could also stop the Pi booting at all, if it happens to run into a problem with the SD card or crash during the resize.
Unfortunately, with no display attached it will be hard to tell what is going on. The main clues will be the LEDs. If the network lights come on then the kernel is definitely running, and if OK is flashing there is still activity on the SD card. If the network lights do not come on then check the OK light for repeating diagnostic code.