Not for long enough to matter. Besides, at the first failure the circuit will no longer meet its specifications for total light output making the whole thing delared broken. People rarely keep a toaster that will only toast one of the two slices.
I've broken a LED or two in my life. They tend to turn into low value resistors at low amounts of destruction. You have to do something fairly major to make the part go open. Merely running some 20-40mA through them backwards is not nearly major enough.
They are typically rated for 5V backwards but may not break down until perhaps as much as 10V. 40mA times 10V is only 0.4W. That will not cause any sort of "BOOM".
It gives you less flicker at the cost of a bridge rectifier. The bridge costs money to install and also has a failure rate so it increases the chance of failure.
If you really care about the flicker, adding another capacitor can reduce it.