Yes - I haven't done this before but have seen a number of stories on these forums that in the US (maybe only applies to certain states), the trade-in value effectively reduces the sale price of the new purchase, and thus, the amount of sales tax charged on the new purchase is less.
I was initially quite surprised about that too, as I assumed that the purchase price for sales tax calculation purposes would remain the same, and the trade-in value is effectively a separate transaction (eg. selling your device to Apple), and you use that credit against the new purchase - but it's all just done simultaneously for ease of transaction.
But it appears that when you do at the same time (or 14 days after purchase where they still allow you to apply trade-in value as refund to credit card, not a gift card separately) you essentially are getting the value of trade-in x (1+tax rate) in trade-in value, which is applied against the full after-tax purchase price of the new Apple device. This is because mathematically, it's the same as if your pre-tax trade-in value is deducted from the pre-tax new device cost, and then you only pay sales tax on the net amount.
