You might be able to get one stream to record in Premiere but certainly not 4. Lossless HD produces huge files, whatever system you end up with, will need to have a vey fast HDD array.
Please define "losslessly". An uncompressed HD stream is ginormous, let alone 4 at once. BlackMagic can record to the BlackMagic M-JPEG codec which is far smaller and will "look good". As Richard said, Premiere is not set up to record multiple channels, just one at a time. You would need a software app made specifically for the BMD multi-channel capture, plus a fast RAID (two 7200 drives in RAID 0 can handle 4 compressed HD streams). I don't know if BMD supplies such an app with the hardware?
I have no experience with Deck Link Quad, but have used the Matrox VS4 in conjunction with Telestream Wirecast software, which allowed me to capture 4 HD-SDI streams at once using the Matrox MPEG-2 I-Frame HD codec (intra-frame, 4:2:2 color, 100-300Mbps data rate). You can get the new VS4 Recorder software bundled with the VS4 hardware, or use Wirecast for the capture (unless that now requires VS4 Recorder also, not sure if that may have changed).
In any case, NO capture card buffers the video, always recorded live to the hard drive directly. Once the stream or streams are recorded, the resulting clips can be edited in Premiere using the MultiCam feature.
Safe Harbor Computers
Thanks for the quick reply. Jeff, yes, truly lossless, no compression. I know something like M-JPEG would look fine for most things but I have a bunch of engineers telling me that we need to get the best possible picture from all 4 cameras. Based on what you've said it doesn't seem like I'll be using Premier so i'll move over to the BMD forums.