I think the first question to ask is: is there a board where, if player A never does anything (and controls the shuffles), player B cannot win?

For this, some calculations. So the idea is to have a useless kingdom (maybe all Villages or something) so you are limited to basic Treasures. But we add Bandit Camp! So basic Treasures are worth negative VP.

So we start with 7 Coppers. Player B only ever gets the highest-value Treasure they could possibly buy. As long as the average coin per hand is less than or equal to 5, it will be possible to arrange the shuffle in a way to only give $5 or less hands, forcing to buy another Silver. After adding s Silvers, your average $ per turn is 5*(7 + 2s)/(10 + s). This is larger than 5 if s > 3. Thus, adding 4 Silvers allows you to get at least 1 Gold every 5 shuffles.

Now start adding Golds until your money density is high enough for Provinces. Current money total is 15, and total cards in deck are 14. We now want that 5*(15 + 3g)/(14 + g) > 7. This is the case when g > 23/8. We need to add 3 Golds and then are guaranteed to get Provinces. Of course adding a Province lowers money density, so we have to get more Golds to make up for it. How many? We want a Gold-per-Province ratio such that the average money density remains at least 7, i.e. 5*3g/(p + g) >= 7, or g/p >= 7/8. So to add 8 Provinces, we're adding 7 more Golds.

Now, we added 4 Silvers and 10 Golds total. With Bandit Fort, that's -28 VP. We have a total of 32 cards, with Wall that's another -17 VP, so -45 VP total, but all the Provinces are worth 48 VP, which is still a net profit of 3VP.

Possible ways to improve to really get a stalemate situation:

- add Heirlooms. With Cursed Gold, you'd effectively have 1 Copper less to Start with. But it also means the kingdom includes Pooka, i.e. trashing, which probably implies that we can be more efficient for Wall points - the shuffle might be able to force "useless Pooka", i.e. a Pooka always paired with 3 Estates and Cursed Gold, but that means that the rest of the draws will be better, so is probably not viable. Lucky Coin might work, but Fool is hard to account for.

- Wolf's Den? For our strategy it doesn't really do anything, but maybe there's a way to get some negative VP out of this? In conjunction with Heirlooms possibly?

- other kingdom cards that influence the setup, but I can't think of any that would make a difference.

Anyway since the "easy" case is already very hard to do, I strongly believe that the answer to 1) and 2) is no.