I'm not practically trying it out, but what will happen if / is full ??

Are there any security risks involved with this??

I've experienced / full

The progs which require writing to disk simply won't work

Can it lead to a security vulnerability??

perhaps yes...

Well, your root isn't sposed to be gettin full, and that's one of the reasons to have separate /var and /tmp dirs and run some script like "diskcheck".
If it's full (and no separate /var) you can only delete before writing, and if it's full on bootup I guess it'll be in essence like a ro system, no write access to /etc, /var, no initlvl, no time, no pid's, no logs no wtmp, etc, etc unless you could make some ramdisk and mount /var in it.
I guess it is a threat, because it will cripple normal operation of the box and requires human intervention to fixit.