I have not used Apple since the Apple II days and have been a Linux only user for many years, but...
You would not be getting the benefit of the firewall in the router, of course. But you *would* still get any functions of the Mac firewall that you noted in your question.
Remember that if this is/was a laptop and you used it at a cafe then you would be just as exposed to the other cafe patrons. Very few in comparison to the whole internet, but still exposed. What is the Mac solution to security when using public Wi-Fi?
You would want to look into settings that tell your computer that it is on a public connection instead of "Home/Private/whatever".
Sonic is not going to recommend running this way, but you are not talking about doing so for an extended period, you are talking about running for days while waiting for a new router.
In your situation I would not be afraid to do so, but I would also be shutting down all services that I run on the LAN (apache, samba, etc.) and would switch to a fully closed host based firewall while waiting for a new router. I would do that *before* hooking up so that I don't even have seconds of running without a firewall that I am comfortable with.
I *wish* I could run this way in that situation, but I am on FTTN and thus cannot use anything but an AT&T router and would thus be hard down while waiting.