If I'm understanding the question right, then the answer's no: once you transfer the money to the Bitpay card, then it's in dollars. The exchange rate is whatever the highest bid is at Bitstamp the second you press the button "Add Funds."
But if you're thinking BTC's likely to keep going up and don't want to transfer much into dollars on the card, that's fine: just keep basically $0 on the card until just before you're going to buy something, then move only that amount of money onto the card.
A Real Life Example
MPS gf: "MPS, is it OK if I go shopping with Carrie and Jen this Saturday?"
MPS: "OK? It's better than OK; I'll be left in peace with crypto and college football!"
MPS gf, now smiling: "Um, well, yeah, I wasn't actually asking permission to see my friends. This isn't 1950. But, [and here her smile turns into that cute, imploring, "I'm young and beautiful and vulnerable, what ever would happen to me in an emergency without the protection of money?" look, which I have never been able to resist. Of course, she knows this.
MPS: "Oh, right, the card. Yeah, sure, go crazy. How much should I put on it?"
MPS gf: "Oh baby, don't worry, I'll take care of that. I know you've got a ton of work tonight."
[the sound of the foyer drawer opening and my wallet being pillaged for its Bitpay card.]
2 weeks later, after a routine review of my Bitpay transactions, down at The Parrot, my local bar, w/ a couple friends
MPS: "700 phucking dollars? How the phuck is that even possible? All she bought was some clothes and shoes and sh!t. Boys, I'll tell you one thing: that cute, eyes wide, vulnerable pose thing she does is never gonna work on me again!
[laughter from MPS' mates, as they've heard that claim before].