No, not exactly. It depends how much is the amount of the item 1 and item 2 before the tax.
If the amount of item 1 before VAT is 10 and the amount of item 2 before VAT is 100, then the VAT for the shipping would be (( 7.7% * 10 + 3.8% *100) - (10 + 100))/(10 +100) ~ 4.15% (if I didn't make any mistake in my calculs) . The function getAverageProductsTaxRate in Cart.php does the same calculation, I think.