No, 970 Pro is a 4x device, installing it on a PCIe 2.0 x16 don't change this fact.
To get any M2 drive past ~1400MB/s when installed in a MP3,1/4,1/5,1 you need an adapter with a PCIe 3.0 switch like Highpoint SSD7101-A or Amfeltec Squid 3.0 to convert PCIe 2.0 x16 into PCIe 3.0 x4.Not even the IOCrest card can get the full speed of a Samsung 970 since it's a 8x card, but it's near.
BTW, don't forget that MP3,1 don't support NVMe, APFS nor configures the PCIe slots for 5GT/s automatically. You will have to hack the BootROM for NVMe and APFS support and configure the slots at every boot to 5GT/s. I would try to find a cheap MP4,1…