I don't claim to undestand it (at all).
You appear to understand it better than you think you do.
But, if they ALWAYS hit it, i suppose they could find a matching block with every single attempt, earning a reward of 25 BTC (currently) in the process.
The difficult level gets recalibrated every 2160 blocks. But if you were stretching the realms of impossibility, they /could/ still continue finding these matching blocks.
Mining with GPUs, they could get a hash rate of say 200MH/s. With only a total of 6929999 blocks getting BTC rewards, they could find them all in a second. (I don't know, technically, whether there needs to be some network or time delay in order for the discovered blocks to be propagated and difficulty redadjusted).
So after your characters' brief burst of impossible luck, that would leave an astronomical difficulty level for the rest of the network which doesn't have the happy plot-device of lady luck shining on them.
The network might well not be able to find any blocks for the next 100 years. Which means no transactions get confirmed. And the difficulty will only adjust to a reasonable rate after 2160 more blocks are found. Disaster! And ironically, they wouldn't even be able to spend their BTCs.
You hit it exactly on the nose.
If they ALWAYS hit . . .
If the luck were taken out...if they ALWAYS hit (for lack of a better word), what is the fastest rate the coins could be generated. Remember, limited hardware but the luck factor is removed in their favor for a period of time. Any element of the process that is due to chance they always hit on the first try.
Then they would generate every single block as fast as their hardware could build the blocks (probably finishing after a few seconds). As such, they'd end up with all the remaining bitcoins (a bit over 9.19 million bitcoins). Then whenever their luck ran out, the bitcoin network would screech to a halt as blocks stopped being solved for years at a time (100's of years at a time?), probably resulting in bitcoins being worthless.