I’m not certain of how AP vouchers work these days (whether you receive a voucher number to link in MDE or a “not yet activated” AP number to link) but you will need some proof of purchase linked to your account in order to access the Passholder page with current discounts. You won’t need to have activated the AP to book a room, but you will likely need to show the activated AP at check in. (As a Passholder for many years, I can’t always predict when I will be asked to show my AP at check in. And I am not sure if online check-in is allowed for an unactivated AP.)
AP Resort Discounts have really fluctuated since pre-pandemic days. Typical savings now is ~5% more than whatever is offered to the general public. Or different resorts may be offered to AP than those offered to GP. Pre-2020, I could always assume I’d receive an AP discount for my preferred resort for my dates. That is no longer the case.
Thus the “break-even” (or better yet, “savings”) point for an AP should never factor in resort discounts (or merch or food for that matter) because those perks can go away at any time. The deciding factor should be ticket cost. If you plan to visit at least twice in a year (or 10+ days in one visit), add up the cost of individual Park Hoppers for those visits and if the total cost is more than the cost of an AP, an AP is the better value.
Then any discounts are gravy!