If you're asking about chance, then sure, there's a chance they may never be mined.. It depends on the transaction pool, how long you want to wait, and what miners are willing to accept.
I've done 0 gwei free transactions before, and I've had problems with 20 gwei transactions never being mined. It depends.
If you're sending thousands of separate transactions, you're not really using cryptocurrency very intelligently. There are better, and cheaper ways.