In most cases a firewall has little additional value over a router just using NAT. Nat because it is stupid and does not know which internal machine to send traffic to unless you port map it will just drop it. That is pretty much the same as a rule that says no inbound traffic which is recommended on firewalls.
The thing the firewall does when there are no rules is it protects the router itself. It will automatically detect some of the common attacks like half open sessions or packet fragmentation attacks. Pretty much it makes it harder for someone to crash your router but it can not stop the more common attack of data flooding which eats all your bandwidth since it has to come all the way to your house for the firewall to see it and the damage is already done.
It does not hurt to have the firewall turned on but it is very unlikely someone is going to try to crash your router anyway, they would much rather attack a server that maybe they could steal something from.
In general a firewall is more used to protect a server that you have exposed intentionally to the internet. If for example you had a web server you could protect it from some of the more common attacks. The other use is if you needed to limit internal machines from accessing stuff on the internet but that would require you to put rules in.