Is there a way to see the text of tty7 without shutting down Xorg?

I presume you want to see the X server logs for your GUI under VT7 (Ctrl+Alt+F7). In other words, the text that gets printed if you were to do a text boot, login and type "startx" (before the script hands over to your DE).

If this is the case, you can simply open your Xserver logs:

less /var/log/Xorg.0.log

For boot logs that would appear prior to the console login & X greeter, check:

less /var/log/boot.log

The greeter creates its own logs. If you're using lightdm (the default greeter), then you'll find them all under:

/var/log/lightdm/

If you start X manually (startx or xinit) you'll see the text in whatever VT you issued the command in - unless you redirect it to a file or /dev/null (remember there are two streams here, stdout and stderr).

Usually however X is started automatically at boot by some display-manager (e.g. gdm, kdm or xdm), so you'll find the information in the Xorg-, *dm-, boot- and upstart-logs under /var/log. Other logs - like /var/log/messages and /var/log/syslog - may also hold some information.