Yes, pickaxe or any destruction tool, no lockpick.
Lockpicking will act as normal but its not linked to the challenge. I have found that sometimes the loot is generous, othertimes stingy, but I have succeeded with the Patrol Car challenge on all my playthoughs. Usually take it on when I get a steel club and something (thats not a pipe weapon) that can spit bullets if need be.
//is there anything that actually happens with the storyline, ...
For the storyline, not as yet. The story is real, in that I have something in mind, in this release its a foundation to set the stage for if/when they introduce bandits. May also end up with a custom map for the storyline.
There will be an update in a few days that includes increasing the number of towns and their size in generated maps and integrated learn-by-use - where half the weapons/miner stat increases are learn-by-use and the other half you purchase normally using the Perk system. (may spin that off as a modlet as well)
cheers