We run 4.11 under Classic at my work every day, unfortunately. There are a few issues to work around.
First, it won't work if the user running it doesn't own the folder and have write permission on all of the files in it. On the plus side, you don't need to run Quark's POS installer for each copy you need on a given machine, you can copy the original QX4 folder to each user. On each machine at my work, in addition to the staff member's user, we have an IT user with administrator privileges, and keep the master Quark copy for the machine in IT's Public folder. Then when Quark inevitably screws up a user's copy, they know to delete their copy and go into ~it/Public and copy the QX411 folder from there into their own user's Applications directory.
Secondly, the fonts all look like crap, but it turns out you can still run ATM in your Classic System, and that half-fixes the problem. You'll still occasionally need to zoom out and zoom back in to force it to regenerate the font glyphs, but that usually fixes the problem. We do have a problem where Classic will occasionally appear to lock up every few days, but I can't tell if it's just Quark being crashy or because we're using ATM which isn't technically supposed to work at all.
Palettes sometimes vanish. if a palette is not completely on top of a Quark window, it will occasionally disappear. You have to close & reopen them by the menu to get them back. I think it's easier to just stretch the Quark window to completely cover the screen, but my Production guys can't stand that.
Also, Quark windows sometimes don't realize they've been clicked on if you try to click them to bring Quark to the foreground when you're working in a native OS X application. Command-tabbing out of Quark and then back will usually make Quark realize it's in the foreground.
Update: Someone on one of my mailing lists pointed me at ClassicDraw XT which is a donationware Quark XTension that is supposed to fix the redraw issue. More later after I've had a chance to test it.