Your line of thinking is spot on : 02 and giffgaff only share the same masts ; they aren't the same company, so unless you use your 02 before coming to giffgaff you'll lose it. You could donate it to charity, though, to save it being wasted.
I don't know if you have a sim already, or if you do where you ordered it from, but if you order one from a member's banner in their signature offering a free sim it will come with £5 free credit on activation. If you order one from the main website it has no credit. £5 isn't a massive sum of money, but it's better than nothing.