No, sorry.
The bandwidth available from a PCIe slot is determined by the PCIe version (in this case 2.0) and the number of "lanes" it has. Each "lane" in PCIe 2.0 offers throughput of up to 500 MB/s.
Your "2.0 x16 (blue)" slot has 16 PCIe lanes. That permits throughput of up to 8 GB/s. (That's 16 times 500 MB/s.)
Your "x16 (x4 mode, black)" slot is the size of the "2.0 x16 (blue)" slot but it only has four PCIe "lanes" in it. That's what "x4 mode" means. So, even though it is able to physically accept x16 cards, its throughput will be limited to 2 GB/s.
Now... depending on what you're doing with the card, that might not matter. But if you're running high-performance games, I expect you'd notice the difference. I doubt it would be as severe as a reduction in frame rate to just 25%, but a reduction to 50% wouldn't be unexpected.
I should probably mention that you are already not getting all the performance from that card that you're paying for, because it is a PCIe 3.0 card. PCIe 3.0 provides almost twice the throughput per lane as PCIe 2.0 (985 MB/s per lane vs. 500). The tests you may have seen for the card's performance assume that you're using it in a PCIe 3.0 slot. So it will not run as fast as indicated in those reports in a 2.0 slot. Most video cards in most applications are not actually using all the bandwidth PCIe offers, so the difference may not matter much, but it's something to keep in mind. The only way to fix that is to get a motherboard that has PCIe 3.0. (While you're at it you could get one in which a long PCIe x16 card won't block the SATA ports. ;) )
Could you provide some explanation and/or references with your answer? As it is, your answer is quite short and difficult to understand. Try to formulate your answer as a piece of knowledge, which can be read on its own. – agtoever – 2015-09-29T07:38:49.737
@agtoever better now? – Jamie Hanrahan – 2015-09-29T09:07:09.293
Great job! +1... – agtoever – 2015-09-29T09:23:36.143
@agtoever Cool, thank you for the +1, and for the nudge. – Jamie Hanrahan – 2015-09-29T09:57:44.077
If he has a P67 motherboard he probablly has a sandy bridge CPU. If so then he will need to upgrade both CPU and motherboard to get PCIe 3.0. – plugwash – 2019-06-28T14:43:41.113