Can customers pay for preorders with a gift card? (Essent Preorder Back in Stock app)

Not while the campaign uses a Shopify selling plan. Shopify doesn't accept gift cards for items bought with a preorder selling plan. This is a Shopify rule, so no preorder app can change it.

If gift cards matter more to you, turn the selling plan off for that campaign: Preorder → Settings → open the campaign → Offer tab → Use selling plan → untick Use Shopify selling plan (purchase option) → Save. Preorders then check out as normal orders, and gift cards work.

You lose these with the selling plan off: partial payments, the app's own preorder discount, and On hold or Scheduled fulfilment. Use Shopify discounts instead.

Full guide: Turn off selling plans for a preorder campaign.