Can a bundled product be variable?

No, because a ‘bundled product’ is a product type and a ‘variable product’ is a product type, therefore a bundled product can never be a variable product.

However it is possible to add variable products to the bundle.

Does the plugin consider the on-sale price or regular price when calculating the price of the bundle?

The plugin calculates the bundle price starting from the regular price and not the sale price.
This because the bundle is already an offer (you can provide discounts on bundled items by setting the discount field in the bundled item). Getting the Regular price, so, is intentional, as this avoids to double-discount the products. Therefore, it’s correct that the plugin doesn’t get the Sale Price of bundled items, since it¬†always gets the Regular Price.