I don't know, I didn't try it myself. Worst case, they'll say "no".
I do think it's unfair, especially when upgrade is for full price. If there would be big discount to go from L3 to L4, then ok, let it die with the board. But for $45, it's not nice. And if you'd have bought standalone x86 license, then according to manual:
Can I move the license to another HDD ?
If your current HDD drive is destroyed, or can no longer be used, it is possible to transfer the license to another HDD. You will have to request a replacement key (see below) which will cost 10$
What is a Replacement Key
It is a special key which is issued by the Support Team if you accidently lose the license, and the Mikrotik Support decides that it is not directly your fault. It costs 10$ and has the same features as the key that you lose. Note that before issuing such key, the Mikrotik Support can ask you to prove that the old drive is failed, in some cases this means sending us the dead drive.
So you could work with that, because in a way, your current "HDD" did break and it was not your fault.